Method and Apparatus for Quadrature Signal Modulation

ABSTRACT

Methods and apparatus for facilitating wireless communication using digital Quadrature Amplitude Modulation are disclosed. A mapping module electronic component of a wireless communication device utilizes a signal constellation for quadrature modulating a signal for transmission or quadrature demodulating a received signal. The signal constellation includes multiple constellation symbols and associated bit sequences. Specific signal constellations are disclosed. The signal constellations may be obtained through an optimization procedure which accounts for both phase noise and power amplifier nonlinearity.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/095,787, entitled “Method and Apparatus for Quadrature SignalModulation,” filed on Mar. 11, 2016, which is a continuation of PCTApplication No. PCT/CN2016/078101, entitled “Method and Apparatus forQuadrature Signal Modulation,” filed on Mar. 31, 2016, whichapplications are hereby incorporated herein by reference.

TECHNICAL FIELD

The present invention pertains to the field of wireless communications,and in particular to a method and apparatus for performing quadratureamplitude modulation, using particular quadrature amplitude modulationconstellations.

BACKGROUND

Quadrature amplitude modulation (QAM) has found extensive applicationsin wired and wireless digital communications systems. In a digital QAMscheme, the QAM constellations are specified by both their amplitude andphase in a quadrature coordination. Phase-shift keying (PSK) modulationcan be considered as a special case of QAM where the amplitude of a PSKmodulation scheme is constant and the PSK constellations are equallyspaced on a circle.

The aim of digital QAM is to communicate a message from a transmitter toa receiver. However, such communication must contend with the presenceof noise, such as thermal noise and phase noise, as well as otherlimitations such as transmitter power limitations. Phase noise(frequency offset) is particularly problematic at higher frequencies,such as 60 GHz and above, and can be generated due to imperfectoscillators in both transmitter and receiver. Use of higher-order QAM inthe presence of thermal noise, phase noise, and other limitations, canresult in unacceptably high error rates, particularly forhigher-frequency communication systems.

Therefore, there is a need for a method and apparatus for quadratureamplitude modulation that obviates or mitigates one or more limitationsof the prior art.

This background information is provided to reveal information believedby the applicant to be of possible relevance to the present invention.No admission is necessarily intended, nor should be construed, that anyof the preceding information constitutes prior art against the presentinvention.

SUMMARY

An object of embodiments of the present invention is to provide a methodand apparatus for quadrature signal modulation in a wirelesscommunication system. In accordance with embodiments of the presentinvention, there is provided a method for facilitating wirelesscommunication using digital Quadrature Amplitude Modulation, the methodcomprising: translating between constellation symbols and bit sequencescorresponding to the constellation symbols using a mapping moduleelectronic component of a wireless communication device, in accordancewith a signal constellation having a specified number of constellationpoints, the constellation symbols used in modulating a signal fortransmission or detected in a received signal, or both, wherein each ofthe constellation symbols is specified in a row of one of Tables 17-26Cas set forth herein, wherein normalized magnitudes of in-phasecomponents of the constellation symbols are specified in one of the “X”and “Y” columns of said one of the tables and normalized magnitudes ofquadrature components of the constellation symbols are specified to a ina different one of the “X” and “Y” columns of said one of the tables. Invarious embodiments, the signal constellation is specified by the valuesin the Tables as rounded or truncated to three, four, five or sixdecimal places. In some embodiments, the signal constellation may beselected from one of a plurality of Tables 17-26C. In variousembodiments, the particular bit sequences associated with theconstellation symbols are as listed in Tables 17-26C, or are derivedfrom the bit sequences listed in Tables 17-26C by adding a constantbinary value to the listed bit sequences, by applying consistent bitreordering operation to the listed bit sequences, or both.

In accordance with embodiments of the present invention, there isprovided an apparatus for a wireless communication device configured forwireless communication using digital Quadrature Amplitude Modulation,the apparatus comprising: a mapping module electronic componentconfigured to translate between bit sequences and correspondingconstellation symbols in accordance with a signal constellation having aspecified number of constellation points, the constellation symbols usedin generating a signal for transmission or detected in a receivedsignal, or both, wherein each of the constellation symbols is specifiedin a row of a one of Tables 17-26C as set forth herein, whereinnormalized magnitudes of in-phase components of the constellationsymbols are specified in one of the “X” and “Y” columns of said one ofthe tables and normalized magnitudes of quadrature components of theconstellation symbols are specified to a in a different one of the “X”and “Y” columns of said one of the tables. In various embodiments, thesignal constellation is specified by the values in the tables as roundedor truncated to three, four, five or six decimal places. In someembodiments, the signal constellation may be selected from one of aplurality of Tables 17-26C. In various embodiments, the particular bitsequences associated with the constellation symbols are as listed inTables 17-26C, or are derived from the bit sequences listed in Tables17-26C by adding a constant binary value to the listed bit sequences, byapplying consistent bit reordering operation to the listed bitsequences, or both.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages of the present invention will becomeapparent from the following detailed description, taken in combinationwith the appended drawings, in which:

FIG. 1 illustrates a wireless transmitter communication apparatus inaccordance with an embodiment of the present invention.

FIG. 2 illustrates a wireless receiver communication apparatus inaccordance with another embodiment of the present invention.

FIG. 3 illustrates a method for wireless transmission of QAM symbols, inaccordance with an embodiment of the present invention.

FIG. 4 illustrates a method for wireless reception of QAM symbols, inaccordance with an embodiment of the present invention.

FIG. 5 illustrates a mapping module electronic component in accordancewith embodiments of the present invention.

FIG. 6 illustrates the generation of a physical layer protocol data unit(PPDU) from a physical layer service data unit (PSDU) in a singlecarrier physical layer, in accordance with an IEEE 802.11ad wirelesscommunication approach which may be utilized in embodiments of thepresent invention.

FIG. 7 illustrates an IEEE 802.11ad single carrier physical layer frameformat and associated block structure which may be utilized inaccordance with embodiments of the present invention.

FIG. 8 illustrates a 16-point signal constellation in accordance with anembodiment of the present invention.

FIG. 9 illustrates a 32-point signal constellation in accordance with anembodiment of the present invention.

FIG. 10A illustrates a 64-point signal constellation in accordance withan embodiment of the present invention.

FIG. 10B illustrates a 64-point signal constellation in accordance withanother embodiment of the present invention.

FIG. 10C illustrates a 64-point signal constellation in accordance withanother embodiment of the present invention.

FIG. 10D illustrates a 64-point signal constellation in accordance withanother embodiment of the present invention.

FIG. 11A illustrates the first quadrant of a 128-point signalconstellation in accordance with an embodiment of the present invention.

FIG. 11B illustrates the first quadrant of a 128-point signalconstellation in accordance with another embodiment of the presentinvention.

FIG. 11C illustrates the first quadrant of a 128-point signalconstellation in accordance with another embodiment of the presentinvention.

FIG. 11D illustrates the first quadrant of a 128-point signalconstellation in accordance with another embodiment of the presentinvention.

FIG. 12A illustrates the first quadrant of a 256-point signalconstellation in accordance with an embodiment of the present invention.

FIG. 12B illustrates the first quadrant of a 256-point signalconstellation in accordance with another embodiment of the presentinvention.

FIG. 12C illustrates the first quadrant of a 256-point signalconstellation in accordance with another embodiment of the presentinvention.

FIG. 13 illustrates a 16-point signal constellation in accordance withanother embodiment of the present invention.

FIG. 14 illustrates a 32-point signal constellation in accordance withanother embodiment of the present invention.

FIG. 15A illustrates a 64-point signal constellation in accordance withanother embodiment of the present invention.

FIG. 15B illustrates a 64-point signal constellation in accordance withanother embodiment of the present invention.

FIG. 15C illustrates a 64-point signal constellation in accordance withanother embodiment of the present invention.

FIG. 15D illustrates a 64-point signal constellation in accordance withanother embodiment of the present invention.

FIG. 16A illustrates the first quadrant of a 128-point signalconstellation in accordance with another embodiment of the presentinvention.

FIG. 16B illustrates the first quadrant of a 128-point signalconstellation in accordance with another embodiment of the presentinvention.

FIG. 16C illustrates the first quadrant of a 128-point signalconstellation in accordance with another embodiment of the presentinvention.

FIG. 16D illustrates the first quadrant of a 128-point signalconstellation in accordance with another embodiment of the presentinvention.

FIG. 17A illustrates the first quadrant of a 256-point signalconstellation in accordance with another embodiment of the presentinvention.

FIG. 17B illustrates the first quadrant of a 256-point signalconstellation in accordance with another embodiment of the presentinvention.

FIG. 17C illustrates the first quadrant of a 256-point signalconstellation in accordance with another embodiment of the presentinvention.

FIG. 18 illustrates the standard derivation of residual phase noise vs.SNR using a linear interpolation phase noise mitigation method inaccordance with an embodiment of the present invention.

FIG. 19 illustrates transmitter and receiver systems in accordance withan embodiment of the present invention.

FIG. 20 illustrates a simplified soft limiter for enforcing a peak powerconstraint, in accordance with an embodiment of the present invention.

FIG. 21 illustrates a theoretical spectral efficiency according to anembodiment of the present invention.

FIG. 22 illustrates a theoretical spectral efficiency according toanother embodiment of the present invention.

FIG. 23 illustrates a constellation optimization procedure according toan embodiment of the present invention.

It will be noted that throughout the appended drawings, like featuresare identified by like reference numerals.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Embodiments of the present invention are directed to a method andapparatus for wireless communication using a digital QAM signalconstellation as described herein. The method includes modulating and/ordemodulating a signal according to the described constellation, using awireless transmitter and/or receiver, or associated signal processingelectronics. The apparatus includes a wireless transmitter and/orreceiver, or associated signal processing electronics, configured tomodulate and/or demodulate a signal according to the describedconstellation. As used herein, QAM refers generally to any amplitudemodulation which includes an in-phase component and a quadraturecomponent, for modulating two carrier signals which are in quadraturewith each other. For example, phase-shift keying is regarded as aparticular form of QAM.

Embodiments of the present invention may be used to wirelesslycommunicate information between a transmitter and receiver. Theinformation can include control plane data, application data, or usermessaging data, for example. On the transmitter side, the information isinitially represented as a plurality of binary digits (bits), andmodulating the signal comprises mapping a given number m of bits at atime to a corresponding symbol in the signal constellation. On thereceiver side, the information is represented via a quadrature modulatedwaveform, and demodulating the signal comprises mapping portions of thewaveform corresponding to a symbol in the signal constellation to anassociated sequence of m bits.

Embodiments of the present invention apply high order modulationschemes, in which each of M=2^(m) symbols in a QAM modulation representsmultiple (m>1) bits. Table 1 shows the spectral efficiency r=mr_(c) andrequired minimum Signal to Noise Ratio (SNR) based on the Shannoncapacity limit, corresponding to different code rates r_(c) and todifferent cardinalities of constellation sets M=2^(m), m=2, . . . , 8.

m 2 3 4 5 6 7 8 min min min min min min min r SNR r SNR r SNR r SNR rSNR r SNR r SNR r_(c) 1/2 1.00 0.0 1.50 2.6 2.00 4.8 2.50 6.7 3.00 8.53.50 10.1 4.00 11.8 5/8 1.25 1.4 1.88 4.3 2.50 6.7 3.13 8.9 3.75 11.04.38 13.0 5.00 14.9 3/4 1.50 2.6 2.25 5.7 3.00 8.5 3.75 11.0 4.50 13.45.25 15.7 6.00 18.0 7/8 1.75 3.7 2.63 7.1 3.50 10.1 4.38 13.0 5.25 15.76.13 18.4 7.00 21.0

In accordance with embodiments of the present invention, and withreference to FIG. 1, a wireless communication apparatus comprising aninput interface 110, a transmitter mapping module 120, and a transmittermodule 130 is disclosed. The input interface 110 is configured toreceive data to be wirelessly transmitted. The data may be representedin binary, and may include at least m bits, where m is the base-2logarithm of the modulation order of the quadrature modulationconstellation being used. The transmitter mapping module 120 isconfigured to receive one or more bit sequences. Each bit sequence isrepresentative of a portion of the data of length m. A bit sequence maycorrespond directly to m contiguous bits of the data, or it may bederived from the data by applying operations such as scrambling,interleaving, channel coding, etc. The transmitter mapping module isfurther configured to generate, for each bit sequence, a correspondingconstellation symbol 122 having an in-phase component 124 and aquadrature component 126. Correspondence between a bit sequence and thegenerated constellation symbol is given according to a particular signalconstellation 128, as described herein. Typically, multiple bitsequences representative of the input data are used to generate asequence of constellation symbols. The transmitter module 130 isconfigured to generate and transmit a wireless signal 135 based on theconstellation symbols generated by the mapping module.

Generation of wireless signals based on constellation symbols can beperformed in a manner as would be readily understood by a worker skilledin the art. For example, a sequence of in-phase components can be usedto amplitude modulate a first sinusoidal carrier signal, and acorresponding sequence of quadrature components can be used to amplitudemodulate a second sinusoidal carrier signal that is out of phase (inquadrature) with the first sinusoidal signal. The sequences of in-phaseand quadrature components can be represented, for example, as pulsetrains or other electrical signals with amplitudes varying according tothe magnitudes of the in-phase and quadrature components, for example,to be used for amplitude modulation of the carrier signals. Theamplitude modulated carrier signals are then added together andtransmitted.

In accordance with embodiments of the present invention, and withreference to FIG. 2, a wireless communication apparatus comprising areceiver module 210, a receiver mapping module 220, and an outputinterface 130 is disclosed. The receiver module is configured to receivea wireless signal 212 and generate constellation symbols 214 based onthe wireless signal, each constellation symbol having an in-phasecomponent 216 and a quadrature component 218. Generation ofconstellation symbols based on a received wireless signal can beperformed in a manner as would be readily understood by a worker skilledin the art. For example, the received signal can be multiplied bylocally generated copies of the carrier signal, low-pass filtering maybe applied to the result, and the output of the low-pass filtering canbe sampled to recover representations of the in-phase and quadraturecomponents of the constellation symbols. The sampling includesquantization. For hard-decision decoding, the receiver mapping module220 is configured to receive constellation symbols 214 and generate, foreach constellation symbol, a bit sequence 228 corresponding to theconstellation symbol. Correspondence between a bit sequence and areceived constellation symbol is given according to a particular signalconstellation 226, as described herein. The output interface 230 isconfigured to provide data 238, a portion of the data represented by thegenerated bit sequence 228 associated with a received constellationsymbol. Alternatively, soft-decision decoding, such as Low DensityParity Check LDPC decoding or turbo decoding may be employed, in which ademodulator outputs a sequence of log-likelihood ratios (LLRs) ratherthan performing direct symbol-to-bit mapping. A decoder then uses theLLR values for decoding.

The provided group of m bits may directly represent m bits of the data,or the portion of data may be obtained at least partially from thegenerated bit sequence by applying operations such as descrambling,deinterleaving, decoding, etc. Typically, the received wireless signalis used to generate a sequence of constellation symbols which are passedto the receiver mapping module. The receiver mapping module thengenerates the data using hard-decision decoding or soft-decisiondecoding.

In accordance with embodiments of the present invention, and withreference to FIG. 3, there is provided a method for facilitatingwireless transmission of QAM symbols. The method includes receiving 310,via an internal input interface of a wireless communication device, datato be wirelessly transmitted. The data may include at least m bits,where m is determined by the modulation order of the quadraturemodulation scheme being used. The method further includes providing 320one or more bit sequences. Each bit sequence is representative of aportion of the data, for example subsequent to operations such as butnot necessarily limited to channel coding. Each bit sequence is oflength m, where m is the predetermined value corresponding to themodulation order. The method further includes determining 330, for eachbit sequence, a corresponding constellation symbol having an in-phasecomponent and a quadrature component. Correspondence between a bitsequence and the provided constellation symbol is given according to aparticular signal constellation, as described herein. Typically,multiple bit sequences representative of the input data are used togenerate a sequence of constellation symbols. The method may furtherinclude generating and transmitting 340 a wireless signal based on thedetermined constellation symbols. The generation of the wireless signalcomprises modulating a carrier signal according to the generatedsequence of constellation symbols.

In accordance with embodiments of the present invention, and withreference to FIG. 4, there is provided a method for performing wirelessreception and demodulation of QAM symbols. The method includes receiving410 a wireless signal and generating 420 received baseband symbols basedon the wireless signal, each received baseband symbol having an in-phasecomponent and a quadrature component. The received baseband symbol caneither generate a bit sequence by mapping the most likely constellationsymbol to a corresponding bit sequence based on the constellationmapping, or form a sequence of bit-related soft values indicating thelikelihood of bit values at the specific bit positions of a bit sequencecorresponding to the selected constellation symbol. As such, the methodfurther includes providing 430 bit sequences or soft valuescorresponding to the received baseband symbol. A received constellationsymbol is given according to a particular signal constellation, asdescribed herein. The method further includes providing 440 data, aportion of the data represented by the provided bit sequence or asequence of soft values associated with a received symbol. The data maybe provided, for example, by performing channel decoding and otheroperations on the bit sequences.

Embodiments of the present invention provide for methods and apparatusfor generating constellation symbols based on bit sequences and/orgenerating bit sequences or sequences of bit-related soft values basedon constellation symbols, according to a correspondence which isspecified by a signal constellation as described herein. Suchembodiments may be represented in the transmitter mapping module andreceiver mapping module described above, collectively referred to asmapping modules. For example, a provided apparatus may receive groups ofm bits and generate constellation symbols, including in-phase andquadrature components, corresponding to the received bit sequences. Bitsequences may be represented by digital signals, such as serial orparallel digital data signals, for example. Sequences of constellationsymbols may be represented, for example, by pairs of electrical signalshaving amplitudes which vary with the magnitudes of the in-phase andquadrature components of the constellation symbols. As another example,sequences of constellation symbols may be represented by time-varyingdigital or analog signals which convey instructions for use by anotherelectronic device to generate such pairs of electrical signals. For areception operation, a provided apparatus may receive pairs ofelectrical signals having amplitudes or other characteristics which areinterpreted, by the apparatus, as the magnitudes of a received sequenceof in-phase and quadrature components of a received sequence ofconstellation symbols. The apparatus may then generate a plurality ofbit sequences or plurality of bit-related soft values in a largersequence, which correspond to the received sequence of constellationsymbols.

Embodiments of the present invention therefore comprise translating, forexample using mapping modules, between constellation symbols and bitsequences according to a particular signal constellation. In the case ofsignal transmission, the translating includes generating constellationsymbols based on bit sequences. In the case of signal reception, thetranslating includes generating bit sequences or bit-related sequencesof soft values based on constellation symbols. Other aspects of signalmodulation and/or demodulation, such as varying the amplitudes ofcarrier signals and/or processing a received signal recoverconstellation symbols, may be, but are not necessarily, included in theembodiments of the present invention.

FIG. 5 illustrates a mapping module electronic component 500 provided inaccordance with embodiments of the present invention. The electroniccomponent may be provided as a semiconductor circuit, for exampleforming part or all of an integrated circuit package. The mapping moduleelectronic component can be configured as a transmitter mapping module,a receiver mapping module, or both. The mapping module includes a firstinterface 510 configured to provide and/or receive groups of m bits. Themapping module further includes a second interface 520 configured toreceive and/or provide signals indicative of constellation symbols. Insome embodiments the second interface may include a first terminal 522for receiving and/or providing in-phase components of the constellationsymbols, and a second terminal 524 for receiving and/or providingquadrature components of the constellation symbols. The mapping moduleis configured to translate, via translation circuitry 530, between bitsequences and constellation symbols according to a signal constellation535. The translation circuitry may be digital or analog circuitry. Insome embodiments, the translation circuitry is preconfigured accordingto a certain signal constellation. In other embodiments, the translationcircuitry is reconfigurable according to a signal constellation whichcan be specified or selected via a control interface 540 of the mappingmodule.

Embodiments of the present invention are applied for signal modulationin millimeter wave (mmWave) wireless communication systems. Someembodiments of the present invention are applicable to signal modulationin Wi-Fi™ communication systems, as specified in the IEEE 802.11 seriesof standards. Some embodiments of the present invention are applicableto signal modulation in wireless communication systems employing acarrier frequency around 60 GHz. It will be readily appreciated thatembodiments of the present invention can be applied to other wirelesscommunication systems, as well as to wired or optical systems, and inother communication environments.

FIG. 6 illustrates the generation of a physical layer protocol data unit(PPDU) from a physical layer service data unit (PSDU) in a singlecarrier physical layer, in accordance with a wireless communicationapproach which may be utilized in embodiments of the present invention.The operations illustrated in FIG. 6 are comparable to those specifiedin the IEEE 802.11ad wireless local area network protocol, and detailscan be found in the IEEE 802.11ad-2012 standards document, publishedDecember, 2012 and having E-ISBN 978-0-7381-8096-0. The single carrierphysical layer may employ low-density parity check (LDPC) codes, forexample with a code word length of 672. The input PSDU data 605undergoes scrambling 610, and the scrambled bits are fragmented 615 toprovide input bits 617. The input bits are then encoded 620, for exampleusing a LDPC code, to provide coded bits 622. An optional interleavingoperation 623 can be performed following encoding. Interleaving caninclude shuffling encoded bits, for example. The coded and possiblyinterleaved bits then optionally undergo zero padding 625. The codedbits, with or without zero padding, are then modulated 630. Inembodiments of the present invention, modulation may be performed usinga signal constellation as described herein. The modulated symbols 632then undergo symbol blocking and guard insertion 635, thereby providingthe PPDU 640. In general, modulation operations according to the presentinvention may be performed after channel coding, such as LDPC coding.

FIG. 7 illustrates an IEEE 802.11ad single carrier physical layer frameformat 700 and associated block structure which may be utilized inaccordance with embodiments of the present invention. A set of threecontiguous data block structures 750 a, 750 b, 750 c are illustrated indetail. The number of data block structures can be variable. Each datablock structure 750 a, 750 b, 750 c in a PPDU includes 448 modulateddata symbols 752 preceded by a guard interval (GI) 755. For multiplecontiguous blocks, groups of 448 modulated data symbols 752 are thusseparated by GIs 755 of the same length-64 bipolar Golay sequence. Thetwo GIs 755 preceding and following a given group of 448 modulated datasymbols 752 form a cyclic prefix permitting FFT/IFFT operations at areceiver to perform frequency-domain equalization. In addition, theknown GIs can be used for other purposes such as phase noise estimationfor mitigation of phase noise.

Embodiments of the present invention relate to signal modulation and/ordemodulation in single carrier systems, for example using the data blockstructure as illustrated in FIG. 7. Embodiments of the present inventionrelate to signal modulation and/or demodulation in single carriersystems with other formats of data block structure.

Embodiments of the present invention relate to signal modulation and/ordemodulation in communication systems with or without phase noise. Phasenoise can significantly degrade the link performance in high-frequencycommunication systems employing high order digital QAM modulations. Thepower spectral density of one model of phase noise considered for IEEE802.11ad is shown in Eq. (1):

$\begin{matrix}{{{PSD}(f)} = {{{{PSD}(0)}\left\lbrack \frac{1 + \left( {f/f_{z}} \right)^{2}}{1 + \left( {f/f_{p}} \right)^{2}} \right\rbrack}.}} & (1)\end{matrix}$

The parameterization of this model as considered for IEEE 802.11ad issuch that: PSD(0)=−90 dBc/Hz; Pole frequency f_(p)=1 MHz; Zero frequencyf_(z)=100 MHz; Corresponding PSD(infinity)=−130 dBc/Hz; and impairmentis modeled at both transmitter and receiver. In embodiments of thepresent invention, signal constellations are provided which have beenconfigured in view of the above phase noise model.

Embodiments of the present invention relate to signal modulation and/ordemodulation in communication systems with or without power amplifiernonlinearity impairments. The power constraints may includepeak-to-average power ratio (PAPR) constraints. A first power amplifiernonlinearity model considered for IEEE 802.11ad is given in Equation(2):

$\begin{matrix}{{{G(A)} = {g\frac{A}{\left( {1 + \left( \frac{gA}{A_{sat}} \right)^{2\; s}} \right)^{\frac{1}{2\; s}}}\mspace{14mu} {in}\mspace{14mu} {RMS}\mspace{14mu} {Volts}}},} & (2)\end{matrix}$

where g is the small signal gain, s is the smoothness factor, andA_(sat) is the saturation level.

A second power amplifier nonlinearity model considered for IEEE 802.11adis given in Equation (3):

$\begin{matrix}{{\Psi (A)} = {\frac{\alpha \; A^{q_{1}}}{\left( {1 + \left( \frac{A}{\beta} \right)^{q_{2}}} \right)}.}} & (3)\end{matrix}$

For Equations (2) and (3) above, CMOS power amplifier model parameterscan be specified as follows. For Equation (2): g=4.65, A_(sat)=0.58 ands=0.81. For Equation (3): α=2560 degrees, β=0.114, q₁=2.4 and q₂=2.3.

In embodiments of the present invention, signal constellations areprovided which have been configured in view of the above power amplifiernonlinearity model.

Embodiments of the present invention include signal constellations whichhave been generated according to a constellation optimization for twoscenarios. The first scenario relates to single carrier systems with alinear channel and without a transmit power constraint. The secondscenario relates to a non-linear channel with nonlinearity impairments.For both scenarios, sub-scenarios which include or exclude phase noiseare considered. In some embodiments, constellations are optimized inview of both the transmit power and phase noise constraints. In variousembodiments the phase noise model and the PA model used for theconstellation optimization are given in Equations (1)-(3) above.Multiple sets of 16-, 32-, 64-, 128- and 256-point constellations may begenerated using this optimization approach. Selected ones of theseconstellations are disclosed herein.

It is noted that a constellation that is considered optimal for aparticular code rate is not limited for use with that code rate. Rather,a constellation can be used for various code rates, even if it has beenoptimized for use with a particular code rate. The use of theconstellation for different code rates may result in a reduction inperformance and/or loss of optimality. More generally, it is noted thata constellation that is considered optimal for a particular set ofconditions can be used in other conditions, with a possible reduction inperformance and/or loss of optimality. However, such a performancereduction may be acceptable. Further, the reduced complexity due to theability to use the same constellation under different conditions mayresult in a benefit which offsets the performance reduction.

Various signal constellations provided in accordance with embodiments ofthe present invention are described in detail below. Each signalconstellation represents a set of constellation symbols. A signalconstellation having M points is referred to as an M-pointconstellation. In various embodiments, the x coordinate value of aconstellation symbol indicates the (normalized) magnitude of thein-phase component of the constellation symbol, and the y coordinatevalue of a constellation symbol indicates the (normalized) magnitude ofthe quadrature component of the constellation symbol. Alternatively, thex coordinate value of a constellation symbol may indicate the(normalized) magnitude of the quadrature component of the constellationsymbol, and the y coordinate value of a constellation symbol indicatesthe (normalized) magnitude of the in-phase component of theconstellation symbol. A sequence of m bits may be associated with eachconstellation symbol.

In some cases, only the first quadrant of a constellation is specified.As such, in some embodiments, the locations of constellation symbols inother quadrants of the constellation can be readily obtained from theconstellation symbols in the first quadrant by reflection symmetry. Forreflection symmetry, given constellation symbols in the first quadrant,the locations of constellation symbols in the second quadrant can beobtained by reflection in the Y (vertical) axis. More specifically, thereflection operation can include, for each constellation symbol in thefirst quadrant specified by vector location (x,y), obtaining aconstellation symbol in the second quadrant specified by vector location(−x, y). Similarly, given constellation symbols in the first quadrant,the locations of constellation symbol in the third quadrant can beobtained by reflection in the Y axis, followed by reflection in the X(horizontal) axis. More specifically, the reflection operation caninclude, for each constellation symbol in the first quadrant specifiedby vector location (x,y), where x and y are non-negative values,obtaining a constellation symbol in the third quadrant specified byvector location (−x,−y). Similarly, given constellation symbols in thefirst quadrant, the locations of constellation symbol in the fourthquadrant can be obtained by reflection in the X (horizontal) axis. Morespecifically, the reflection operation can include, for eachconstellation symbol in the first quadrant specified by vector location(x,y), obtaining a constellation symbol in the second quadrant specifiedby vector location (x, −y). Alternatively to obtain constellationsymbols in different quadrants from those of the first quadrant by thereflection operations above, a series of reflection operations can beused. For example, the constellation symbols in the second quadrant canbe obtained from those of the first quadrant by reflection in the Yaxis, the constellation symbols in the third quadrant can be obtainedfrom those of the second quadrant by reflection in the X axis, and theconstellation symbols in the fourth quadrant can be obtained from thoseof the third quadrant by reflection in the Y axis. As used herein, theterm “reflection symmetric constellation symbols” refers to a set offour constellation symbols (x,y), (x,−y), (−x,−y), (−x,y) for givenvalues of x and y.

As used herein, the term “symmetric constellation symbols” refers to“reflection symmetric constellation symbols”. A constellation consistingof reflection symmetric constellation symbols may also be referred to asa reflection symmetric constellation, or as a “symmetric constellation”.

In various embodiments, the illustrated signal constellations can bescaled by a nonzero scaling factor k. Scaling of a signal constellationcan be performed by mapping each constellation symbol (x,y) in theconstellation to a new constellation symbol (kx,ky). The (x,y)coordinate values illustrated in FIGS. 8-17C and specified in Tables17-26C are nominal. In Tables 17-21C constellation magnitudes arenormalized such that the average power, across all constellationsymbols, is equal to one. In Tables 22-26C, constellation magnitudes arenormalized such that the power of each constellation symbol is less thanor equal to one. The specified coordinate values may alternatively benormalized such that the peak power, among all constellation symbols, isequal to one. The present description of the specified constellationsshould be understood to include other scalings or normalizationsthereof, for example as would be readily understood by a worker skilledin the art.

In various embodiments, the (x,y) locations of constellation symbols inthe illustrated signal constellations can be varied by a limited amount.For example, when the locations of constellation symbols are specifiedin one embodiment with a precision of d decimal places, anotherembodiment may correspond to the same general locations of constellationsymbols, but specified with a precision of d−1 decimal places, anotherembodiment correspond to the same general locations of constellationsymbols but specified with a precision of d−2 decimal places, and yetanother embodiment correspond to the same general locations ofconstellation symbols but specified with a precision of d−3 decimalplaces. The lower precision embodiment can be obtained from the higherprecision embodiment through rounding or truncation. In variousembodiments, the normalized (x,y) locations of the constellation symbolscan be specified to 3, 4, 5, or 6 decimal places. A magnitude that isdefined by a coordinate value to at least d decimal places of precisionis a magnitude which, when measured, agrees with the coordinate value toat least d decimal places of precision, further decimal places of themeasurement and/or coordinate value being either discarded viatruncation or subjected to a rounding operation to the d^(th) decimalplace.

In some embodiments, the precision of the decimal places may be relatedto Error Vector Magnitude (EVM) requirement, taking into account factorssuch as I/Q arm amplitude and phase balance, DC offset, and phase noise.In IEEE 802.11ad, EVM is typically required to be as low as −21 dB forsingle carrier transmissions and −26 dB for OFDM transmissions.

As another example, when the locations of constellation symbols arespecified in a first embodiment with a precision of d decimal places, asecond embodiment may correspond to the same general locations ofconstellation symbols, but varied by up to δ units, where δ is on theorder of 10^(−d), or alternatively 10^(−d+1) or 10^(−d+2), so that, forexample, given a constellation symbol (x,y) in the first embodiment, thesecond embodiment may include a corresponding constellation symbol(x′,y′), where (x−δ,y−δ)<(x′,y′)<(x+δ,y+δ), or alternatively where˜(x′,y′)−(x,y)∥<δ.

In embodiments of the present invention, the normalized magnitudes ofthe constellation symbols are defined by coordinates which fall anywherewithin a rectangular region, including along a boundary of therectangular region. For each constellation symbol, the rectangularregion is defined by a first corner specified by a first coordinate pairand a second corner specified by a second coordinate pair. The secondcorner is diagonally opposite the first corner. For a signalconstellation as specified in one of Tables 17-26C, and for each listedcoordinate pair in the table, the first coordinate pair (specifying thefirst corner of the rectangular region) can be derived from the listedcoordinate pair by rounding down both X and Y values of the listedcoordinate pair. The second coordinate pair (specifying the secondcorner of the rectangular region) can be derived from the listedcoordinate pair by rounding up both X and Y values of the listedcoordinate pair. In some embodiments, rounding is performed to thenearest thousandth, as would be readily understood by a worker skilledin the art. In some embodiments, rounding is performed to the nearestten thousandth. In some embodiments, rounding is performed to thenearest hundred thousandth.

As such, for each of original Tables 17-26C, a new table can be definedin which the “X” column of the original table is replaced with a pair ofcolumns “Xmin” and “Xmax,” and the “Y” column of the original table isreplaced with a pair of columns “Ymin” and “Ymax.” The “Xmin” and “Ymin”columns list the X and Y values of the first coordinate pairs, and the“Xmax” and “Ymax” columns list the X and Y values of the secondcoordinate pairs. The new table indicates a set of ranges for theconstellation symbols, such that the normalized magnitude of eachconstellation symbol has an X coordinate value lying between a valuespecified in a corresponding row of the “Xmin” column and a valuespecified in the same row of the “Xmax” column, and further such thatthe normalized magnitude of the constellation symbol has a Y coordinatevalue lying between a value specified in the same row of the “Ymin”column and a value specified in the same row of the “Ymax” column. Suchnew tables are not explicitly listed in the present disclosure for thesake of brevity, however they can be readily derived as described aboveby a person skilled in the art.

In some embodiments, rather than determining the corners of therectangular regions via rounding, the first corner of the rectangularregion can be derived from the listed coordinate pair by subtracting afirst predetermined value from the X value of the listed coordinatepair, and subtracting a second predetermined value from the Y value ofthe listed coordinate pair. The second coordinate pair specifying thesecond corner of the rectangular region can be derived from the listedcoordinate pair by adding the first predetermined value to the X valueof the listed coordinate pair, and adding the second predetermined valueto the Y value of the listed coordinate pair. The first and secondpredetermined values can be values which are less than or equal to0.0005, for example.

In addition to specifying the vector locations of the constellationsymbols in the XY plane, embodiments of the present invention specifythe bit sequences corresponding to each of the constellation symbols. Aswill be readily understood by a worker skilled in the art, given aninput group of m bits, modulation includes identifying a symbol in thesignal constellation corresponding to the bit sequence, and modulating asignal according to the identified symbol. Similarly, demodulation of areceived signal includes identifying a symbol in the signalconstellation most closely corresponding to a given portion of thereceived signal, and outputting the bit sequence corresponding to theidentified symbol or the bit-related sequence of soft valuescorresponding to the constellation. The correspondence between a signaland a constellation symbol may be such that, where the signal is locallydescribable by the function A cos(ωt)+B sin(ωt), the correspondingconstellation symbol is the closest constellation symbol in the XY planeto point (A,B).

In various embodiments, each group of m bits includes twoquadrant-specifying bits. The quadrant-specifying bits may be at fixedlocations in the bit sequence. For example, the first two bits (mostsignificant bits) of a bit sequence may be the quadrant-specifying bits.The remaining m−2 bits of a bit sequence are referred to as quadrantnon-specific bits. In some embodiments, the quadrant specifying bitscorresponding to all constellation symbols in the first quadrant are 00,the quadrant specifying bits corresponding to all constellation symbolsin the second quadrant are 10, the quadrant specifying bitscorresponding to all constellation symbols in the third quadrant are 11,and the quadrant specifying bits corresponding to all constellationsymbols in the fourth quadrant are 01.

In various embodiments, the quadrant non-specific bits (for example them−2 least significant bits) of each given constellation symbol may beidentical to the quadrant non-specific bits of each other constellationsymbol within the same set of symmetric constellation symbols as thegiven constellation symbol.

It will be readily understood that the correspondence between bitsequences and constellation symbols can be varied in several ways. Forexample, each of the illustrated bit values inverted, such that a “0”bit becomes a “1” and vice versa. As another example, the illustratedbit positions can be re-ordered. The reordering may be a consistent bitreordering, i.e. in which the same reordering is applied to all bitsequences in a constellation. A simple example of a reordering is areversal of all bits, for example such that group abcd is replaced bygroup dcba. As yet another example, a constant value can be added toeach of the illustrated bit sequences using a modulo-M binary additionoperation, where M=2^(m) and m is the number of bits in each bitsequence. It is noted that bit inversion corresponds to addition of aparticular constant value consisting of all binary ones. A combinationof bit reordering and addition of a constant value may also beperformed.

In some embodiments, for an index value k ranging from k=1 to k=2^(m−2)inclusive, where m is the number of bits in each bit sequence: thequadrant non-specific bits of the bit sequence corresponding to theconstellation symbol defined by a k^(th)-listed one of the coordinatepairs are equal to: a binary representation of k−1; the binaryrepresentation of k−1 added to a constant value under Modulo-2^(m−2)addition; the binary representation of k−1 subjected to a consistent bitreordering, or the binary representation of k−1 added to a constantvalue under Modulo-2^(m−2) addition and subjected to the consistent bitreordering.

It is noted that, in Tables 17-26C, the bit sequences associated withthe constellation symbols correspond to binary representations of theposition of the constellation symbol in the list. For example, thefirst-listed constellation symbol is associated with bit sequence ‘0 . .. 000’, the second-listed constellation symbol is associated with bitsequence ‘0 . . . 001’, etc.

In various embodiments, bit sequences are assigned to constellationsymbols using a Gray mapping. Gray mapping comprises associating bitpatterns (bit sequences) with constellation symbols, such that the bitsequences associated with adjacent constellation symbols differ by onlyone bit. That is, the bit sequences assigned to the constellationsymbols closest to a first constellation symbol differ by one bit fromthe bit sequence assigned to the first constellation symbol. Twodimensional Gray mapping comprises associating bit sequences withconstellation symbols, such that the bit sequences associated withadjacent constellation symbols differ by only one bit, and the bitsequences associated with the next nearest constellation symbols differby two bits. The term “adjacent” can be taken to mean closest in termsof a distance metric applied to constellation points in the signalconstellation.

FIG. 8 illustrates a 16-point signal constellation provided inaccordance with an embodiment of the present invention. Thecorresponding (x,y) coordinate values of the constellation symbolsillustrated in FIG. 8 are provided to six decimal places in Table 17.The signal constellation of FIG. 8 is optimized for use with a code rateof 3/4, and is also suitable for use with other code rates. The coderate corresponds to a channel code which is applied to the bit sequencesprior to mapping to constellation symbols for transmission, and which isused for decoding to recover the coded information bits. In FIGS. 8-17C,bit sequences (according to some embodiments of the present invention)are shown generally above their corresponding constellation points.Ambiguities can be resolved by reference to the corresponding tables.

FIG. 9 illustrates a 32-point signal constellation provided inaccordance with an embodiment of the present invention. Thecorresponding (x,y) coordinate values of the constellation symbolsillustrated in FIG. 9 are provided to six decimal places in Table 18.The signal constellation of FIG. 9 is optimized for use with a code rateof 3/4 and is also suitable for use with other code rates.

FIGS. 10A to 10D illustrate four different 64-point signalconstellations provided in accordance with embodiments of the presentinvention. The corresponding (x,y) coordinate values of theconstellation symbols illustrated in FIGS. 10A to 10D are provided tosix decimal places in Tables 19A to 19D, respectively. The signalconstellation of FIG. 10A is optimized for use with a code rate of 5/8and is also suitable for use with other code rates. The signalconstellation of FIG. 10B is optimized for use with a code rate of 3/4and is also suitable for use with other code rates. The signalconstellation of FIG. 10C is optimized for use with a code rate of 13/16and is also suitable for use with other code rates. The signalconstellation of FIG. 10D is optimized for use with a code rate of 7/8and is also suitable for use with other code rates.

FIGS. 11A to 11D illustrate the first quadrants of four different128-point signal constellations provided in accordance with embodimentsof the present invention. The corresponding (x,y) coordinate values ofthe constellation symbols illustrated in FIGS. 11A to 11D are providedto six decimal places in Tables 20A to 20D, respectively. The signalconstellation of FIG. 11A is optimized for use with a code rate of 5/8and is also suitable for use with other code rates. The signalconstellation of FIG. 11B is optimized for use with a code rate of 3/4and is also suitable for use with other code rates. The signalconstellation of FIG. 11C is optimized for use with a code rate of 13/16and is also suitable for use with other code rates. The signalconstellation of FIG. 11D is optimized for use with a code rate of 7/8and is also suitable for use with other code rates.

FIGS. 12A to 12C illustrate the first quadrants of three different256-point signal constellations provided in accordance with embodimentsof the present invention. The corresponding (x,y) coordinate values ofthe constellation symbols illustrated in FIGS. 12A to 12C are providedto six decimal places in Tables 21A to 21C, respectively. The signalconstellation of FIG. 12A is optimized for use with a code rate of 3/4and is also suitable for use with other code rates. The signalconstellation of FIG. 12B is optimized for use with a code rate of 13/16and is also suitable for use with other code rates. The signalconstellation of FIG. 12C is optimized for use with a code rate of 7/8and is also suitable for use with other code rates.

The constellations described above with respect to FIGS. 8-12C andTables 17-21C were initially derived by an optimization operation whichproduced signal constellations optimized for single carrier scenariosexhibiting phase noise impairment, but without power amplifiernonlinearity. However, the constellations are not necessarily limited touse in such scenarios.

FIG. 13 illustrates a 16-point signal constellation provided inaccordance with an embodiment of the present invention. Thecorresponding (x,y) coordinate values of the constellation symbolsillustrated in FIG. 13 are provided to six decimal places in Table 22.The signal constellation of FIG. 13 is optimized for use with a coderate of 3/4 and is also suitable for use with other code rates.

FIG. 14 illustrates a 32-point signal constellation provided inaccordance with an embodiment of the present invention. Thecorresponding (x,y) coordinate values of the constellation symbolsillustrated in FIG. 14 are provided to six decimal places in Table 23.The signal constellation of FIG. 14 is optimized for use with a coderate of 3/4 and is also suitable for use with other code rates.

FIGS. 15A to 15D illustrate four different 64-point signalconstellations provided in accordance with embodiments of the presentinvention. The corresponding (x,y) coordinate values of theconstellation symbols illustrated in FIGS. 15A to 15D are provided tosix decimal places in Tables 24A to 24D, respectively. The signalconstellation of FIG. 15A is optimized for use with a code rate of 5/8and is also suitable for use with other code rates. The signalconstellation of FIG. 15B is optimized for use with a code rate of 3/4and is also suitable for use with other code rates. The signalconstellation of FIG. 15C is optimized for use with a code rate of 13/16and is also suitable for use with other code rates. The signalconstellation of FIG. 15D is optimized for use with a code rate of 7/8and is also suitable for use with other code rates.

FIGS. 16A to 16D illustrate the first quadrants of four different128-point signal constellations provided in accordance with anembodiment of the present invention. The corresponding (x,y) coordinatevalues of the constellation symbols illustrated in FIGS. 16A to 16D areprovided to six decimal places in Tables 25A to 25D, respectively. Thesignal constellation of FIG. 16A is optimized for use with a code rateof 5/8 and is also suitable for use with other code rates. The signalconstellation of FIG. 16B is optimized for use with a code rate of 3/4and is also suitable for use with other code rates. The signalconstellation of FIG. 16C is optimized for use with a code rate of 13/16and is also suitable for use with other code rates. The signalconstellation of FIG. 16D is optimized for use with a code rate of 7/8and is also suitable for use with other code rates.

FIGS. 17A to 17C illustrate the first quadrants of three different256-point signal constellation provided in accordance with embodimentsof the present invention. The corresponding (x,y) coordinate values ofthe constellation symbols illustrated in FIGS. 17A to 17C are providedto six decimal places in Tables 26A to 26C, respectively. The signalconstellation of FIG. 17A is optimized for use with a code rate of 3/4and is also suitable for use with other code rates. The signalconstellation of FIG. 17B is optimized for use with a code rate of 13/16and is also suitable for use with other code rates. The signalconstellation of FIG. 17C is optimized for use with a code rate of 7/8and is also suitable for use with other code rates.

The constellations described above with respect to FIGS. 13-17C andTables 22-26C were initially derived by an optimization operation whichproduced signal constellations which were believed to be optimal forsingle carrier scenarios exhibiting both phase noise and power amplifiernonlinearity impairments. However, the constellations are notnecessarily limited to use in such scenarios.

The (x,y) coordinate values provided in Tables 17-26C are specified to alevel of precision of six decimal places. In some embodiments, thecoordinate values of the constellation symbols illustrated in FIGS.8-17C and shown in Tables 17-26C can be truncated to a level ofprecision of three, four, or five decimal places.

Embodiments of the present invention provide for a method and apparatusfor performing wireless communication using digital Quadrature AmplitudeModulation. The method and apparatus involve utilizing, by a mappingmodule electronic component of a wireless communication device, a signalconstellation for modulating a signal for transmission or demodulating areceived signal, the signal constellation comprising a plurality ofconstellation symbols. The signal constellation may be obtained using anoptimization procedure for example as described below. It is noted thatthe optimization procedure below is not intended to limit the disclosedsignal constellations. Rather, the optimization procedure is provided asan example of how these and similar constellations may be obtained, andthe circumstances under which they may be expected to perform well.

In a practical system, phase noise may be said to have a memory. Thatis, the state of the phase noise at a given time may depend on the stateof the phase noise at previous times. As such, according to embodimentsof the present invention, the residual phase error caused by theimperfect cancellation for phase noise with memory is obtained based onthe specified pilot distribution and the methods for phase estimationand phase noise mitigation. The residual phase error is assumed to be awhite random process. Therefore, with the aid of transformation of phasenoise with memory to the memoryless residual phase error, methods forconstellation optimization with white phase noise constraint and whiteGaussian noise can be applied to constellation optimization in thepresence of a constraint representing phase noise with memory.

One embodiment of the present invention provides for signalconstellations derived from conducting a joint signal-labelingoptimization for the optimized modulation symbol constellations eitherwith phase noise constraint only or with both phase noise and powerconstraints with a simplified optimization algorithm in order to obtainthe constellations of higher order modulation such those having 128 or256 points.

Another embodiment of the present invention provides for signalconstellations derived from the optimization of pilot sequencedistribution in a single carrier system, which depends on a given phasenoise model such as described in Equation (1) as well as particular SNRlevel, overhead ratio, and phase estimate and phase noise mitigationalgorithms.

According to an embodiment of the present invention, a simple andefficient algorithm for the estimation of the phase noise based on thepresence of a pilot field of length L every W transmitted symbols, witha pilot overhead OH=L/W may be utilized. The output of the channelaffected by the phase noise θ_(k) and thermal noise n_(k) may be writtenas:

r _(k) =e ^(jθ) ^(k) p _(k) +n _(k)

If the known pilot symbols are placed in contiguous positions

k ε [nW−L/2, nW+L/2],

with arbitrary integer n, a phase estimate corresponding to the middleof the pilot field can be calculated as follows:

$\begin{matrix}{{\hat{\theta}}_{n\; W} = {{\tan^{- 1}\left( \frac{\sum\limits_{k = {{nW} - {L/2}}}^{{nW} + {L/2} - 1}\; {\left( {r_{k}p_{k}^{*}} \right)}}{\sum\limits_{k = {{nW} - {L/2}}}^{{nW} + {L/2} - 1}\; {\Re \left( {r_{k}p_{k}^{*}} \right)}} \right)}.}} & (4)\end{matrix}$

To derive a sequence of phases between two consecutive phase estimatescalculated using Equation (4), that is the (nW)th and ((n+1)W)^(th)phase estimates, the following linear interpolation formula is used:

$\begin{matrix}{{{\hat{\theta}}_{{n\; W} + m} = {{\left\lbrack \frac{W - m}{W} \right\rbrack {\hat{\theta}}_{n\; W}} + {\left\lbrack \frac{m}{W} \right\rbrack {\hat{\theta}}_{{({n + 1})}W}}}}{{m = 1},\ldots \mspace{14mu},{W - 1.}}} & (5)\end{matrix}$

For a given overhead OH=L/W, the optimal length of the pilot field L canbe obtained by trading off accuracy of the estimation Equation (4)versus accuracy of interpolation Equation (5). As shown in FIG. 7, in anIEEE 802.11ad Single Carrier (SC) block, the pilot field length L=64 andthe single SC block length W=512. Therefore, OH=64/512=12.5%.

After mitigation of phase noise, the power spectral density (PSD) of theresidual phase error is assumed to be white. Standard deviation ofresidual phase noise σ_(φ) is used to evaluate the phase errors after aphase noise mitigation process and is used to optimize theconstellations. FIG. 18 shows the standard derivation of residual phasenoise vs. SNR using the linear interpolation phase noise mitigationmethod (5). The standard deviation of the residual phase noise (leftvertical axis) versus SNR for a system baud rate R_(s)=2 GHz, and apilot overhead of 12.5% is shown. The solid line curve corresponds tothe 802.11ad SC frame structure (L=64, W=512). The dashed curvecorresponds to the optimal pilot distribution. The dotted curve showsthe optimal pilot field length (to be read in the right vertical axis).

Performance of a given signal constellation over a channel under idealdetection and decoding can be computed using the Mutual Information(MI):

$\begin{matrix}{{MI} = {E\left\lbrack {\log \frac{P\left( {ZW} \right)}{P(Z)}} \right\rbrack}} & (6)\end{matrix}$

or using the Pragmatic Mutual Information (PMI):

$\begin{matrix}{{PMI} = {\sum\limits_{i = 1}^{m}\; {{E\left\lbrack {\log \frac{P\left( {ZB_{i}} \right)}{P(Z)}} \right\rbrack}.}}} & (7)\end{matrix}$

FIG. 19 illustrates transmitter and receiver systems bounded by the PMI.In the FIG. 19 as well as the above Equations (6) and (7), W and Zrepresent the input and output of channel respectively and B_(i) is thei^(th) bit in W. The MI provides an upper bound on the maximum spectralefficiency, defined as r=mr_(c), where m is the number of bitsassociated to each modulation symbol and r_(c) is the binary code rate.However, in practical systems optimization of signal constellations isperformed under the PMI approach. To improve the performance ofpragmatic systems, the mapping of bits to constellation can be suitablyoptimized, for example using Gray mapping. Although the PMI can be ingeneral quite different from the MI, the difference can be reducedsignificantly when using optimized constellations and bit-to-signalmappings.

The computation of PMI can be performed with numerical techniques whenthe conditional distribution of the channel P(Z|W) is known. When thechannel is memoryless, the output at a given time instant only dependson the corresponding input at the same time and the computation of PMIbecomes easier. Practical memoryless channel models include AWGN andWhite phase noise channels.

In channels constrained by the use of a nonlinear amplifier theoptimization of the constellation may be appropriately modified. Inthese cases, the AM/AM curve of the non-linearity may be representedusing the simplified soft limiter shown FIG. 20 by enforcing a peakpower constraint. Peak power of the constellation may then become arelevant parameter.

The following system conditions were used in the computation of signalconstellations according to an optimization procedure. Signalconstellations with 16, 32, 64, 128 and 256 modulation points wereconsidered. Five code rates: r_(c)=1/2, 5/8, 3/4, 13/16, 7/8 wereconsidered. Channel scenarios were considered corresponding to AWGNwithout phase noise, AWGN with minimal residual phase noisecorresponding to the optimal pilot distribution, AWGN with residualphase noise corresponding to the standard (64/512) pilot distribution;AWGN with non linearity, AWGN with non linearity and minimal residualphase noise corresponding to optimal pilot distribution, and AWGN withnon linearity and residual phase noise corresponding to the standard(64/512) pilot distribution. The non linearity is represented using aPeak Signal-to-Noise ratio (PSNR) constraint.

According to embodiments of the present invention, for each pair of coderate and constellation size, as well as for various levels of theresidual phase noise, a constellation and the corresponding binarylabeling are designed to achieve a PMI larger than the target spectralefficiency r=mr_(c) with the minimum possible SNR or PSNR.

FIG. 21 is a graph showing the loss in spectral efficiency (from theShannon limit (in bits per dimension) as a function of the channel SNR,for square QAM type constellations (M=2^(2q)) with Bit Interleaved CodedModulation (BICMm) (a Pragmatic Mutual Information (PMI) approach),according to an embodiment of the present invention. The plotdemonstrates that when using a BICM approach, each constellation set hasan optimal range of SNR for practical uses.

FIG. 22 is a graph showing the loss in spectral efficiency from theShannon limit (in bits per dimension) as a function of the spectralefficiency, according to an embodiment of the present invention. In FIG.22 it is observed that the crossing point for optimality between thedifferent constellation happens roughly at spectral efficienciesr=(q−0.4) bit per dimension, where q is the number of bits associated toeach signal of the constellation.

From this observation it is possible to determine the optimal range ofcoding rates for 2^(2q) QAM constellation with BICM:

(q−1.4)/q<r _(c) ^(q)<(q−0.4)/q.

In some embodiments, the optimal range may be further reduced by alsoimplementing the cross QAM constellations with size M=2^(2q+1). That is,non-square QAM constellations may be utilized in addition to square QAMconstellations.

In some embodiments, a 16-point constellation or a 32-pointconstellation, for example having a code rate of 3/4, is used when0.3<r_(c) ^(q)<0.8. In some embodiments, a 64-point constellation or a128-point constellation, for example having a code rate of 5/8, 3/4,13/16 or 7/8 is used when 0.53<r_(c) ^(q)<0.87. In some embodiments, a256-point constellation, for example having a code rate of 3/4, 13/16 or7/8 is used when 0.65<r_(c) ^(q)<0.9.

Given modulation format, code rate and channel scenario, constellationand bit sequence labeling can be optimized to minimize SNR to achieve aPMI greater than the target spectral efficiency r=mr_(c). FIG. 23illustrates an applicable constellation optimization procedure using asimulated annealing (SA) technique, according to an embodiment of thepresent invention. Embodiments of the present invention involveproviding a signal constellation which is derived from a simulatingannealing algorithm which is applied to maximize Pragmatic MutualInformation. The algorithm may use a logarithmic, polynomial, or othercooling function. The polynomial cooling function may be particularlyappropriate for higher order modulations, such as order 64 and above.

Tables 2-16 illustrate numerical results indicative of performance ofthe corresponding signal constellations disclosed herein in Tables17-26C and FIGS. 8-17C, compared to the performance of conventional QAMconstellations. These signal constellations were evaluated numericallyto obtain the illustrated results. The results were obtained undercertain assumptions and are provided by way of example only, and withthe understanding that performance may vary in practice.

Performance in Tables 2-16 is reported in terms of SNR or PSNR, asappropriate, to achieve the target spectral efficiencies, for the QAMand selected optimized constellations. Tables 2-4 relate to 16-pointconstellations, Tables 5-7 relate to 32-point constellations, Tables8-10 relate to 64-point constellations, Tables 11-13 relate to 128-pointconstellations, and Tables 14-16 relate to 256-point constellations.Tables 2, 5, 8, 11 and 14 show the performance of square QAMconstellations used as a basis for comparison. Tables 3, 6, 9, 12 and 15show the performance of the selected (optimized) constellationsaccording to embodiments of the invention. Tables 4, 7, 10, 13 and 16show the gains in dB of the selected (optimized) constellationsdisclosed herein with respect to their closest corresponding QAMconstellation and each of these tables can be obtained by subtractionperformed on the two tables immediately preceding it.

In Tables 2-16 each performance result has been obtained using aconstellation optimized for the system scenario corresponding to thephase noise, pilot signal, and power amplifier conditions indicated inthe table.

Tables 2-16 show performance gains that are believed to be significantin a significant number of cases, especially in the case of PSNR.

TABLE 1 Performance (I) of QAM versus selected optimized constellationswith 16 points. SQUARE QAM CONSTELLATION SNR PSNR CODE PN PN RATE NO PNPN OPT STD NO PN PN OPT STD 1/2 5.33 5.38 5.38 7.86 7.96 7.96 5/8 7.307.40 7.42 9.87 9.93 9.99 3/4 9.29 9.44 9.51 11.89 11.95 12.01 13/1610.36 10.52 10.54 12.89 13.02 13.11 7/8 11.57 11.73 11.82 14.10 14.2314.35

TABLE 3 Performance (II) of QAM versus selected optimized constellationswith 16 points. EMBODIMENT CONSTELLATION SNR PSNR CODE PN PN RATE NO PNPN OPT STD NO PN PN OPT STD 1/2 5.21 5.33 5.33 6.51 6.58 6.61 5/8 7.177.27 7.27 8.52 8.65 8.65 3/4 9.26 9.33 9.39 10.57 10.70 10.76 13/1610.42 10.52 10.55 11.66 11.86 11.89 7/8 11.87 11.98 12.07 12.88 13.1013.23

TABLE 4 Performance (III) of QAM versus selected optimizedconstellations with 16 points. DIFFERENCE SNR PSNR CODE PN PN RATE NO PNPN OPT STD NO PN PN OPT STD 1/2 0.13 0.05 0.05 1.36 1.38 1.34 5/8 0.130.13 0.14 1.34 1.28 1.34 3/4 0.03 0.11 0.13 1.32 1.25 1.25 13/16 −0.050.00 −0.01 1.23 1.16 1.22 7/8 −0.30 −0.25 −0.25 1.23 1.13 1.13

TABLE 5 Performance (I) of QAM versus selected optimized constellationswith 32 points. SQUARE QAM CONSTELLATION SNR PSNR CODE PN PN RATE NO PNPN OPT STD NO PN PN OPT STD 1/2 7.87 7.93 7.99 10.12 10.24 10.24 5/810.10 10.24 10.32 12.38 12.50 12.57 3/4 12.27 12.42 12.55 14.55 14.6914.82 13/16 13.31 13.56 13.70 15.65 15.81 16.02 7/8 14.55 14.80 15.0216.83 17.05 17.31

TABLE 6 Performance (II) of QAM versus selected optimized constellationswith 32 points. EMBODIMENT CONSTELLATION SNR PSNR CODE PN PN RATE NO PNPN OPT STD NO PN PN OPT STD 1/2 7.37 7.49 7.49 8.99 9.12 9.12 5/8 9.509.62 9.69 11.32 11.49 11.57 3/4 11.77 11.89 11.95 13.80 14.05 14.2713/16 13.02 13.18 13.27 15.27 15.59 15.95 7/8 14.57 14.77 14.89 16.9417.52 18.27

TABLE 7 Performance (III) of QAM versus selected optimizedconstellations with 32 points. DIFFERENCE SNR PSNR CODE PN PN RATE NO PNPN OPT STD NO PN PN OPT STD 1/2 0.50 0.43 0.50 1.13 1.13 1.13 5/8 0.600.62 0.63 1.06 1.01 1.00 3/4 0.50 0.53 0.60 0.75 0.64 0.55 13/16 0.280.38 0.43 0.38 0.22 0.07 7/8 −0.02 0.03 0.13 −0.11 −0.47 −0.95

TABLE 8 Performance (I) of QAM versus selected optimized constellationswith 64 points. SQUARE QAM CONSTELLATION SNR PSNR CODE PN PN RATE NO PNPN OPT STD NO PN PN OPT STD 1/2 9.44 9.56 9.64 13.14 13.20 13.26 5/811.92 12.14 12.17 15.64 15.77 15.89 3/4 14.41 14.66 14.83 18.07 18.2918.54 13/16 15.71 15.99 16.26 19.37 19.59 19.96 7/8 17.06 17.42 17.9120.75 21.03 21.55

TABLE 9 Performance (II) of QAM versus selected optimized constellationswith 64 points. EMBODIMENT CONSTELLATION SNR PSNR CODE PN PN RATE NO PNPN OPT STD NO PN PN OPT STD 1/2 9.01 9.07 9.14 11.01 11.14 11.19 5/811.39 11.55 11.64 13.77 13.94 14.06 3/4 13.94 14.16 14.29 16.54 16.7216.97 13/16 15.46 15.62 15.84 17.84 18.14 18.59 7/8 16.93 17.16 17.4119.28 19.63 20.25

TABLE 10 Performance (III) of QAM versus selected optimizedconstellations with 64 points. DIFFERENCE SNR PSNR CODE PN PN RATE NO PNPN OPT STD NO PN PN OPT STD 1/2 0.42 0.49 0.50 2.13 2.06 2.08 5/8 0.530.59 0.53 1.88 1.83 1.83 3/4 0.47 0.50 0.55 1.53 1.56 1.57 13/16 0.250.38 0.42 1.53 1.45 1.38 7/8 0.13 0.27 0.50 1.47 1.41 1.30

TABLE 11 Performance (I) of QAM versus selected optimized constellationswith 128 points. SQUARE QAM CONSTELLATION SNR PSNR CODE PN PN RATE NO PNPN OPT STD NO PN PN OPT STD 1/2 11.76 11.95 12.07 14.95 15.07 15.20 5/814.39 14.64 14.89 17.56 17.77 18.02 3/4 17.03 17.38 17.78 20.17 20.5020.93 13/16 18.38 18.78 19.47 21.52 21.88 22.60 7/8 19.81 20.34 21.3622.97 23.44 24.56

TABLE 12 Performance (II) of QAM versus selected optimizedconstellations with 128 points. EMBODIMENT CONSTELLATION SNR PSNR CODEPN PN RATE NO PN PN OPT STD NO PN PN OPT STD 1/2 10.70 10.85 10.88 13.2413.45 13.49 5/8 13.52 13.64 13.77 16.17 16.39 16.64 3/4 16.41 16.6316.88 19.28 19.63 20.13 13/16 18.10 18.35 18.72 20.72 21.10 21.72 7/819.73 19.98 20.47 22.24 22.69 23.72

TABLE 13 Performance (III) of QAM versus selected optimizedconstellations with 128 points. DIFFERENCE SNR PSNR CODE PN PN RATE NOPN PN OPT STD NO PN PN OPT STD 1/2 1.06 1.09 1.20 1.70 1.63 1.70 5/80.88 1.00 1.13 1.39 1.38 1.38 3/4 0.63 0.75 0.91 0.89 0.88 0.81 13/160.28 0.43 0.75 0.80 0.78 0.88 7/8 0.08 0.36 0.89 0.73 0.75 0.84

TABLE 14 Performance (I) of QAM versus selected optimized constellationswith 256 points. SQUARE QAM CONSTELLATION SNR PSNR CODE PN PN RATE NO PNPN OPT STD NO PN PN OPT STD 1/2 13.32 13.48 13.60 17.50 17.63 17.82 5/816.26 16.60 16.91 20.48 20.73 21.13 3/4 19.31 19.73 20.56 23.49 23.8524.81 13/16 20.83 21.46 22.71 25.08 25.50 26.96 7/8 22.48 23.26 25.5126.66 27.35 30.00

TABLE 15 Performance (II) of QAM versus selected optimizedconstellations with 256 points. EMBODIMENT CONSTELLATION SNR PSNR CODEPN PN RATE NO PN PN OPT STD NO PN PN OPT STD 1/2 12.70 12.85 12.98 15.9516.07 16.23 5/8 15.66 15.90 16.13 19.02 19.26 19.60 3/4 18.84 19.1819.68 22.18 22.48 23.23 13/16 20.46 20.86 21.64 23.96 24.33 25.36 7/822.73 23.10 24.01 25.88 26.28 27.65

TABLE 16 Performance (III) of QAM versus selected optimizedconstellations with 256 points. DIFFERENCE SNR PSNR CODE PN PN RATE NOPN PN OPT STD NO PN PN OPT STD 1/2 0.63 0.63 0.63 1.55 1.56 1.59 5/80.60 0.70 0.77 1.45 1.47 1.53 3/4 0.47 0.55 0.88 1.31 1.38 1.58 13/160.38 0.59 1.07 1.13 1.17 1.59 7/8 −0.25 0.16 1.50 0.77 1.07 2.35

Tables 17-26C as referenced herein are presented below. As noted above,each table specifies a signal constellation, with each row specifying aconstellation symbol in which one of the X and Y values indicates anormalized magnitude of the in-phase component of the constellationsymbol and the other of the X and Y values indicates a normalizedmagnitude of the quadrature component of the constellation symbol. Thenormalized magnitudes may be scaled. The first column specifies bitsequences corresponding to the constellation symbols. In someembodiments, the entries in the first column can be reordered. In someembodiments, the entries in the second column can be varied, for exampleby rounding, truncating or varying by up to a predetermined amount.

TABLE 17 SYMBOL COORDINATE BITS X Y 0000 0.208300 0.385859 0001 0.6435290.210665 0010 0.453620 1.186803 0011 1.179606 0.586066 0100 0.208300−0.385859 0101 0.643529 −0.210665 0110 0.453620 −1.186803 0111 1.179606−0.586066 1000 −0.208300 0.385859 1001 −0.643529 0.210665 1010 −0.4536201.186803 1011 −1.179606 0.586066 1100 −0.208300 −0.385859 1101 −0.643529−0.210665 1110 −0.453620 −1.186803 1111 −1.179606 −0.586066

TABLE 18 SYMBOL COORDINATE BITS X Y 00000 1.310029 0.338031 000010.224325 0.876872 00010 0.720578 0.336506 00011 0.269767 0.543938 001001.012286 0.981782 00101 0.423089 1.343637 00110 0.540439 0.139694 001110.159408 0.198087 01000 1.310029 −0.338031 01001 0.224325 −0.87687201010 0.720578 −0.336506 01011 0.269767 −0.543938 01100 1.012286−0.981782 01101 0.423089 −1.343637 01110 0.540439 −0.139694 011110.159408 −0.198087 10000 −1.310029 0.338031 10001 −0.224325 0.87687210010 −0.720578 0.336506 10011 −0.269767 0.543938 10100 −1.0122860.981782 10101 −0.423089 1.343637 10110 −0.540439 0.139694 10111−0.159408 0.198087 11000 −1.310029 −0.338031 11001 −0.224325 −0.87687211010 −0.720578 −0.336506 11011 −0.269767 −0.543938 11100 −1.012286−0.981782 11101 −0.423089 −1.343637 11110 −0.540439 −0.139694 11111−0.159408 −0.198087

TABLE 19A SYMBOL COORDINATE BITS X Y 000000 1.469392 0.279838 0000011.056826 0.221924 000010 0.278986 0.118028 000011 0.715494 0.159574000100 1.278954 0.863275 000101 0.881208 0.583362 000110 0.3132800.160867 000111 0.595671 0.362205 001000 0.295098 1.516036 0010010.173629 1.014971 001010 0.114742 0.259617 001011 0.152038 0.700078001100 0.785642 1.243046 001101 0.550103 0.874280 001110 0.1649750.288326 001111 0.353214 0.596159 010000 1.469392 −0.279838 0100011.056826 −0.221924 010010 0.278986 −0.118028 010011 0.715494 −0.159574010100 1.278954 −0.863275 010101 0.881208 −0.583362 010110 0.313280−0.160867 010111 0.595671 −0.362205 011000 0.295098 −1.516036 0110010.173629 −1.014971 011010 0.114742 −0.259617 011011 0.152038 −0.700078011100 0.785642 −1.243046 011101 0.550103 −0.874280 011110 0.164975−0.288326 011111 0.353214 −0.596159 100000 −1.469392 0.279838 100001−1.056826 0.221924 100010 −0.278986 0.118028 100011 −0.715494 0.159574100100 −1.278954 0.863275 100101 −0.881208 0.583362 100110 −0.3132800.160867 100111 −0.595671 0.362205 101000 −0.295098 1.516036 101001−0.173629 1.014971 101010 −0.114742 0.259617 101011 −0.152038 0.700078101100 −0.785642 1.243046 101101 −0.550103 0.874280 101110 −0.1649750.288326 101111 −0.353214 0.596159 110000 −1.469392 −0.279838 110001−1.056826 −0.221924 110010 −0.278986 −0.118028 110011 −0.715494−0.159574 110100 −1.278954 −0.863275 110101 −0.881208 −0.583362 110110−0.313280 −0.160867 110111 −0.595671 −0.362205 111000 −0.295098−1.516036 111001 −0.173629 −1.014971 111010 −0.114742 −0.259617 111011−0.152038 −0.700078 111100 −0.785642 −1.243046 111101 −0.550103−0.874280 111110 −0.164975 −0.288326 111111 −0.353214 −0.596159

TABLE 19B SYMBOL COORDINATE BITS X Y 000000 1.492905 0.360756 0000011.080694 0.217529 000010 0.403075 0.095458 000011 0.768391 0.154809000100 1.206775 0.854056 000101 0.849704 0.601606 000110 0.4179130.175906 000111 0.610015 0.376978 001000 0.309008 1.471972 0010010.198570 1.031429 001010 0.103390 0.265338 001011 0.134876 0.685577001100 0.824050 1.192733 001101 0.553412 0.861355 001110 0.1746130.295716 001111 0.339582 0.576666 010000 1.492905 −0.360756 0100011.080694 −0.217529 010010 0.403075 −0.095458 010011 0.768391 −0.154809010100 1.206775 −0.854056 010101 0.849704 −0.601606 010110 0.417913−0.175906 010111 0.610015 −0.376978 011000 0.309008 −1.471972 0110010.198570 −1.031429 011010 0.103390 −0.265338 011011 0.134876 −0.685577011100 0.824050 −1.192733 011101 0.553412 −0.861355 011110 0.174613−0.295716 011111 0.339582 −0.576666 100000 −1.492905 0.360756 100001−1.080694 0.217529 100010 −0.403075 0.095458 100011 −0.768391 0.154809100100 −1.206775 0.854056 100101 −0.849704 0.601606 100110 −0.4179130.175906 100111 −0.610015 0.376978 101000 −0.309008 1.471972 101001−0.198570 1.031429 101010 −0.103390 0.265338 101011 −0.134876 0.685577101100 −0.824050 1.192733 101101 −0.553412 0.861355 101110 −0.1746130.295716 101111 −0.339582 0.576666 110000 −1.492905 −0.360756 110001−1.080694 −0.217529 110010 −0.403075 −0.095458 110011 −0.768391−0.154809 110100 −1.206775 −0.854056 110101 −0.849704 −0.601606 110110−0.417913 −0.175906 110111 −0.610015 −0.376978 111000 −0.309008−1.471972 111001 −0.198570 −1.031429 111010 −0.103390 −0.265338 111011−0.134876 −0.685577 111100 −0.824050 −1.192733 111101 −0.553412−0.861355 111110 −0.174613 −0.295716 111111 −0.339582 −0.576666

TABLE 19C SYMBOL COORDINATE BITS X Y 000000 1.223083 0.871183 0000011.501110 0.301512 000010 0.977190 0.129880 000011 1.034515 0.370077000100 0.752034 1.165798 000101 0.670194 0.763847 000110 0.6224850.140135 000111 0.728917 0.432979 001000 0.146134 1.065653 0010010.158150 0.688012 001010 0.128341 0.119548 001011 0.111238 0.401943001100 0.296713 1.461668 001101 0.398918 0.653188 001110 0.3869980.128121 001111 0.372132 0.404640 010000 1.223083 −0.871183 0100011.501110 −0.301512 010010 0.977190 −0.129880 010011 1.034515 −0.370077010100 0.752034 −1.165798 010101 0.670194 −0.763847 010110 0.622485−0.140135 010111 0.728917 −0.432979 011000 0.146134 −1.065653 0110010.158150 −0.688012 011010 0.128341 −0.119548 011011 0.111238 −0.401943011100 0.296713 −1.461668 011101 0.398918 −0.653188 011110 0.386998−0.128121 011111 0.372132 −0.404640 100000 −1.223083 0.871183 100001−1.501110 0.301512 100010 −0.977190 0.129880 100011 −1.034515 0.370077100100 −0.752034 1.165798 100101 −0.670194 0.763847 100110 −0.6224850.140135 100111 −0.728917 0.432979 101000 −0.146134 1.065653 101001−0.158150 0.688012 101010 −0.128341 0.119548 101011 −0.111238 0.401943101100 −0.296713 1.461668 101101 −0.398918 0.653188 101110 −0.3869980.128121 101111 −0.372132 0.404640 110000 −1.223083 −0.871183 110001−1.501110 −0.301512 110010 −0.977190 −0.129880 110011 −1.034515−0.370077 110100 −0.752034 −1.165798 110101 −0.670194 −0.763847 110110−0.622485 −0.140135 110111 −0.728917 −0.432979 111000 −0.146134−1.065653 111001 −0.158150 −0.688012 111010 −0.128341 −0.119548 111011−0.111238 −0.401943 111100 −0.296713 −1.461668 111101 −0.398918−0.653188 111110 −0.386998 −0.128121 111111 −0.372132 −0.404640

TABLE 19D SYMBOL COORDINATE BITS X Y 000000 1.484430 0.355657 0000011.103689 0.241419 000010 0.483043 0.093713 000011 0.757638 0.144839000100 1.150175 0.837105 000101 0.876141 0.599840 000110 0.3359460.248000 000111 0.608728 0.420395 001000 0.255763 1.404577 0010010.189712 1.014604 001010 0.088351 0.457627 001011 0.166639 0.679954001100 0.768973 1.227892 001101 0.588939 0.901538 001110 0.1057570.127560 001111 0.433169 0.631655 010000 1.484430 −0.355657 0100011.103689 −0.241419 010010 0.483043 −0.093713 010011 0.757638 −0.144839010100 1.150175 −0.837105 010101 0.876141 −0.599840 010110 0.335946−0.248000 010111 0.608728 −0.420395 011000 0.255763 −1.404577 0110010.189712 −1.014604 011010 0.088351 −0.457627 011011 0.166639 −0.679954011100 0.768973 −1.227892 011101 0.588939 −0.901538 011110 0.105757−0.127560 011111 0.433169 −0.631655 100000 −1.484430 0.355657 100001−1.103689 0.241419 100010 −0.483043 0.093713 100011 −0.757638 0.144839100100 −1.150175 0.837105 100101 −0.876141 0.599840 100110 −0.3359460.248000 100111 −0.608728 0.420395 101000 −0.255763 1.404577 101001−0.189712 1.014604 101010 −0.088351 0.457627 101011 −0.166639 0.679954101100 −0.768973 1.227892 101101 −0.588939 0.901538 101110 −0.1057570.127560 101111 −0.433169 0.631655 110000 −1.484430 −0.355657 110001−1.103689 −0.241419 110010 −0.483043 −0.093713 110011 −0.757638−0.144839 110100 −1.150175 −0.837105 110101 −0.876141 −0.599840 110110−0.335946 −0.248000 110111 −0.608728 −0.420395 111000 −0.255763−1.404577 111001 −0.189712 −1.014604 111010 −0.088351 −0.457627 111011−0.166639 −0.679954 111100 −0.768973 −1.227892 111101 −0.588939−0.901538 111110 −0.105757 −0.127560 111111 −0.433169 −0.631655

TABLE 20A SYMBOL COORDINATE BITS X Y 0000000 0.737273 0.315203 00000010.782564 0.180128 0000010 0.471801 0.125755 0000011 0.472349 0.0828890000100 0.584038 0.424801 0000101 0.600465 0.414587 0000110 0.4111690.162424 0000111 0.431203 0.128962 0001000 0.113326 0.576184 00010010.132604 0.585352 0001010 0.109346 0.231247 0001011 0.109292 0.1590560001100 0.265381 0.483973 0001101 0.265697 0.558228 0001110 0.1643570.264453 0001111 0.142192 0.229753 0010000 0.987276 0.501105 00100011.073123 0.189336 0010010 1.238487 0.575437 0010011 1.328506 0.2316400010100 0.751918 0.674743 0010101 0.679577 0.745095 0010110 1.2489640.961337 0010111 1.793509 0.444665 0011000 0.178513 0.836678 00110010.146379 1.017268 0011010 0.280870 1.717180 0011011 0.220033 1.3213460011100 0.371932 0.779634 0011101 0.467467 0.944880 0011110 0.9330891.379959 0011111 0.606172 1.218326 0100000 0.737273 −0.315203 01000010.782564 −0.180128 0100010 0.471801 −0.125755 0100011 0.472349 −0.0828890100100 0.584038 −0.424801 0100101 0.600465 −0.414587 0100110 0.411169−0.162424 0100111 0.431203 −0.128962 0101000 0.113326 −0.576184 01010010.132604 −0.585352 0101010 0.109346 −0.231247 0101011 0.109292 −0.1590560101100 0.265381 −0.483973 0101101 0.265697 −0.558228 0101110 0.164357−0.264453 0101111 0.142192 −0.229753 0110000 0.987276 −0.501105 01100011.073123 −0.189336 0110010 1.238487 −0.575437 0110011 1.328506 −0.2316400110100 0.751918 −0.674743 0110101 0.679577 −0.745095 0110110 1.248964−0.961337 0110111 1.793509 −0.444665 0111000 0.178513 −0.836678 01110010.146379 −1.017268 0111010 0.280870 −1.717180 0111011 0.220033 −1.3213460111100 0.371932 −0.779634 0111101 0.467467 −0.944880 0111110 0.933089−1.379959 0111111 0.606172 −1.218326 1000000 −0.737273 0.315203 1000001−0.782564 0.180128 1000010 −0.471801 0.125755 1000011 −0.472349 0.0828891000100 −0.584038 0.424801 1000101 −0.600465 0.414587 1000110 −0.4111690.162424 1000111 −0.431203 0.128962 1001000 −0.113326 0.576184 1001001−0.132604 0.585352 1001010 −0.109346 0.231247 1001011 −0.109292 0.1590561001100 −0.265381 0.483973 1001101 −0.265697 0.558228 1001110 −0.1643570.264453 1001111 −0.142192 0.229753 1010000 −0.987276 0.501105 1010001−1.073123 0.189336 1010010 −1.238487 0.575437 1010011 −1.328506 0.2316401010100 −0.751918 0.674743 1010101 −0.679577 0.745095 1010110 −1.2489640.961337 1010111 −1.793509 0.444665 1011000 −0.178513 0.836678 1011001−0.146379 1.017268 1011010 −0.280870 1.717180 1011011 −0.220033 1.3213461011100 −0.371932 0.779634 1011101 −0.467467 0.944880 1011110 −0.9330891.379959 1011111 −0.606172 1.218326 1100000 −0.737273 −0.315203 1100001−0.782564 −0.180128 1100010 −0.471801 −0.125755 1100011 −0.472349−0.082889 1100100 −0.584038 −0.424801 1100101 −0.600465 −0.4145871100110 −0.411169 −0.162424 1100111 −0.431203 −0.128962 1101000−0.113326 −0.576184 1101001 −0.132604 −0.585352 1101010 −0.109346−0.231247 1101011 −0.109292 −0.159056 1101100 −0.265381 −0.4839731101101 −0.265697 −0.558228 1101110 −0.164357 −0.264453 1101111−0.142192 −0.229753 1110000 −0.987276 −0.501105 1110001 −1.073123−0.189336 1110010 −1.238487 −0.575437 1110011 −1.328506 −0.2316401110100 −0.751918 −0.674743 1110101 −0.679577 −0.745095 1110110−1.248964 −0.961337 1110111 −1.793509 −0.444665 1111000 −0.178513−0.836678 1111001 −0.146379 −1.017268 1111010 −0.280870 −1.7171801111011 −0.220033 −1.321346 1111100 −0.371932 −0.779634 1111101−0.467467 −0.944880 1111110 −0.933089 −1.379959 1111111 −0.606172−1.218326

TABLE 20B SYMBOL COORDINATE BITS X Y 0000000 0.779391 0.338303 00000010.705151 0.165321 0000010 0.392817 0.073826 0000011 0.566840 0.0986100000100 0.591096 0.495628 0000101 0.506207 0.386704 0000110 0.3333090.129562 0000111 0.431485 0.259293 0001000 0.133150 0.720478 00010010.112303 0.521489 0001010 0.088988 0.094762 0001011 0.084578 0.3319070001100 0.369721 0.688796 0001101 0.245135 0.489948 0001110 0.1731440.142180 0001111 0.187579 0.326278 0010000 0.960305 0.408119 00100011.024151 0.117108 0010010 1.193232 0.494688 0010011 1.308642 0.1846150010100 0.755084 0.676471 0010101 0.815391 0.852249 0010110 1.2253720.896021 0010111 1.673595 0.351190 0011000 0.153929 0.914118 00110010.210848 1.095014 0011010 0.311339 1.668426 0011011 0.184999 1.3010750011100 0.468118 0.850595 0011101 0.563693 0.998855 0011110 0.9588251.358356 0011111 0.578328 1.241114 0100000 0.779391 −0.338303 01000010.705151 −0.165321 0100010 0.392817 −0.073826 0100011 0.566840 −0.0986100100100 0.591096 −0.495628 0100101 0.506207 −0.386704 0100110 0.333309−0.129562 0100111 0.431485 −0.259293 0101000 0.133150 −0.720478 01010010.112303 −0.521489 0101010 0.088988 −0.094762 0101011 0.084578 −0.3319070101100 0.369721 −0.688796 0101101 0.245135 −0.489948 0101110 0.173144−0.142180 0101111 0.187579 −0.326278 0110000 0.960305 −0.408119 01100011.024151 −0.117108 0110010 1.193232 −0.494688 0110011 1.308642 −0.1846150110100 0.755084 −0.676471 0110101 0.815391 −0.852249 0110110 1.225372−0.896021 0110111 1.673595 −0.351190 0111000 0.153929 −0.914118 01110010.210848 −1.095014 0111010 0.311339 −1.668426 0111011 0.184999 −1.3010750111100 0.468118 −0.850595 0111101 0.563693 −0.998855 0111110 0.958825−1.358356 0111111 0.578328 −1.241114 1000000 −0.779391 0.338303 1000001−0.705151 0.165321 1000010 −0.392817 0.073826 1000011 −0.566840 0.0986101000100 −0.591096 0.495628 1000101 −0.506207 0.386704 1000110 −0.3333090.129562 1000111 −0.431485 0.259293 1001000 −0.133150 0.720478 1001001−0.112303 0.521489 1001010 −0.088988 0.094762 1001011 −0.084578 0.3319071001100 −0.369721 0.688796 1001101 −0.245135 0.489948 1001110 −0.1731440.142180 1001111 −0.187579 0.326278 1010000 −0.960305 0.408119 1010001−1.024151 0.117108 1010010 −1.193232 0.494688 1010011 −1.308642 0.1846151010100 −0.755084 0.676471 1010101 −0.815391 0.852249 1010110 −1.2253720.896021 1010111 −1.673595 0.351190 1011000 −0.153929 0.914118 1011001−0.210848 1.095014 1011010 −0.311339 1.668426 1011011 −0.184999 1.3010751011100 −0.468118 0.850595 1011101 −0.563693 0.998855 1011110 −0.9588251.358356 1011111 −0.578328 1.241114 1100000 −0.779391 −0.338303 1100001−0.705151 −0.165321 1100010 −0.392817 −0.073826 1100011 −0.566840−0.098610 1100100 −0.591096 −0.495628 1100101 −0.506207 −0.3867041100110 −0.333309 −0.129562 1100111 −0.431485 −0.259293 1101000−0.133150 −0.720478 1101001 −0.112303 −0.521489 1101010 −0.088988−0.094762 1101011 −0.084578 −0.331907 1101100 −0.369721 −0.6887961101101 −0.245135 −0.489948 1101110 −0.173144 −0.142180 1101111−0.187579 −0.326278 1110000 −0.960305 −0.408119 1110001 −1.024151−0.117108 1110010 −1.193232 −0.494688 1110011 −1.308642 −0.1846151110100 −0.755084 −0.676471 1110101 −0.815391 −0.852249 1110110−1.225372 −0.896021 1110111 −1.673595 −0.351190 1111000 −0.153929−0.914118 1111001 −0.210848 −1.095014 1111010 −0.311339 −1.6684261111011 −0.184999 −1.301075 1111100 −0.468118 −0.850595 1111101−0.563693 −0.998855 1111110 −0.958825 −1.358356 1111111 −0.578328−1.241114

TABLE 20C SYMBOL COORDINATE BITS X Y 0000000 0.676205 0.590907 00000010.696016 0.362489 0000010 0.553277 0.064967 0000011 0.641368 0.1955730000100 0.526012 0.596882 0000101 0.490563 0.432520 0000110 0.3723950.089910 0000111 0.433984 0.256395 0001000 0.133129 0.680380 00010010.140357 0.511313 0001010 0.073689 0.113398 0001011 0.073957 0.3428010001100 0.335239 0.697471 0001101 0.293873 0.462352 0001110 0.2234780.122727 0001111 0.250692 0.291177 0010000 0.849307 0.605280 00100010.910806 0.371753 0010010 1.121469 0.096631 0010011 0.889883 0.1008400010100 1.044658 0.689042 0010101 1.351312 0.747663 0010110 1.6535540.212837 0010111 1.334308 0.348076 0011000 0.106020 0.847896 00110010.110430 1.108822 0011010 0.790965 1.102054 0011011 0.991785 1.2773380011100 0.409035 0.918111 0011101 0.191275 1.371272 0011110 0.5807721.045388 0011111 0.545581 1.581968 0100000 0.676205 −0.590907 01000010.696016 −0.362489 0100010 0.553277 −0.064967 0100011 0.641368 −0.1955730100100 0.526012 −0.596882 0100101 0.490563 −0.432520 0100110 0.372395−0.089910 0100111 0.433984 −0.256395 0101000 0.133129 −0.680380 01010010.140357 −0.511313 0101010 0.073689 −0.113398 0101011 0.073957 −0.3428010101100 0.335239 −0.697471 0101101 0.293873 −0.462352 0101110 0.223478−0.122727 0101111 0.250692 −0.291177 0110000 0.849307 −0.605280 01100010.910806 −0.371753 0110010 1.121469 −0.096631 0110011 0.889883 −0.1008400110100 1.044658 −0.689042 0110101 1.351312 −0.747663 0110110 1.653554−0.212837 0110111 1.334308 −0.348076 0111000 0.106020 −0.847896 01110010.110430 −1.108822 0111010 0.790965 −1.102054 0111011 0.991785 −1.2773380111100 0.409035 −0.918111 0111101 0.191275 −1.371272 0111110 0.580772−1.045388 0111111 0.545581 −1.581968 1000000 −0.676205 0.590907 1000001−0.696016 0.362489 1000010 −0.553277 0.064967 1000011 −0.641368 0.1955731000100 −0.526012 0.596882 1000101 −0.490563 0.432520 1000110 −0.3723950.089910 1000111 −0.433984 0.256395 1001000 −0.133129 0.680380 1001001−0.140357 0.511313 1001010 −0.073689 0.113398 1001011 −0.073957 0.3428011001100 −0.335239 0.697471 1001101 −0.293873 0.462352 1001110 −0.2234780.122727 1001111 −0.250692 0.291177 1010000 −0.849307 0.605280 1010001−0.910806 0.371753 1010010 −1.121469 0.096631 1010011 −0.889883 0.1008401010100 −1.044658 0.689042 1010101 −1.351312 0.747663 1010110 −1.6535540.212837 1010111 −1.334308 0.348076 1011000 −0.106020 0.847896 1011001−0.110430 1.108822 1011010 −0.790965 1.102054 1011011 −0.991785 1.2773381011100 −0.409035 0.918111 1011101 −0.191275 1.371272 1011110 −0.5807721.045388 1011111 −0.545581 1.581968 1100000 −0.676205 −0.590907 1100001−0.696016 −0.362489 1100010 −0.553277 −0.064967 1100011 −0.641368−0.195573 1100100 −0.526012 −0.596882 1100101 −0.490563 −0.4325201100110 −0.372395 −0.089910 1100111 −0.433984 −0.256395 1101000−0.133129 −0.680380 1101001 −0.140357 −0.511313 1101010 −0.073689−0.113398 1101011 −0.073957 −0.342801 1101100 −0.335239 −0.6974711101101 −0.293873 −0.462352 1101110 −0.223478 −0.122727 1101111−0.250692 −0.291177 1110000 −0.849307 −0.605280 1110001 −0.910806−0.371753 1110010 −1.121469 −0.096631 1110011 −0.889883 −0.1008401110100 −1.044658 −0.689042 1110101 −1.351312 −0.747663 1110110−1.653554 −0.212837 1110111 −1.334308 −0.348076 1111000 −0.106020−0.847896 1111001 −0.110430 −1.108822 1111010 −0.790965 −1.1020541111011 −0.991785 −1.277338 1111100 −0.409035 −0.918111 1111101−0.191275 −1.371272 1111110 −0.580772 −1.045388 1111111 −0.545581−1.581968

TABLE 20D SYMBOL COORDINATE BITS X Y 0000000 0.752060 0.302196 00000010.788983 0.113122 0000010 0.325356 0.054462 0000011 0.573961 0.0989340000100 0.579122 0.497202 0000101 0.471776 0.396048 0000110 0.2949170.133438 0000111 0.433938 0.245088 0001000 0.132847 0.742015 00010010.122253 0.604949 0001010 0.068657 0.075472 0001011 0.060983 0.4452070001100 0.382346 0.652673 0001101 0.302064 0.494450 0001110 0.1664970.233502 0001111 0.196116 0.340897 0010000 0.907567 0.452354 00100011.043922 0.158157 0010010 1.130081 0.548716 0010011 1.320594 0.1814130010100 0.712483 0.646623 0010101 0.815526 0.865815 0010110 1.1570760.928991 0010111 1.532471 0.508968 0011000 0.120519 0.915797 00110010.148259 1.123784 0011010 0.282652 1.690100 0011011 0.221465 1.3872360011100 0.423824 0.821654 0011101 0.488704 1.037583 0011110 0.8725461.413810 0011111 0.675009 1.247576 0100000 0.752060 −0.302196 01000010.788983 −0.113122 0100010 0.325356 −0.054462 0100011 0.573961 −0.0989340100100 0.579122 −0.497202 0100101 0.471776 −0.396048 0100110 0.294917−0.133438 0100111 0.433938 −0.245088 0101000 0.132847 −0.742015 01010010.122253 −0.604949 0101010 0.068657 −0.075472 0101011 0.060983 −0.4452070101100 0.382346 −0.652673 0101101 0.302064 −0.494450 0101110 0.166497−0.233502 0101111 0.196116 −0.340897 0110000 0.907567 −0.452354 01100011.043922 −0.158157 0110010 1.130081 −0.548716 0110011 1.320594 −0.1814130110100 0.712483 −0.646623 0110101 0.815526 −0.865815 0110110 1.157076−0.928991 0110111 1.532471 −0.508968 0111000 0.120519 −0.915797 01110010.148259 −1.123784 0111010 0.282652 −1.690100 0111011 0.221465 −1.3872360111100 0.423824 −0.821654 0111101 0.488704 −1.037583 0111110 0.872546−1.413810 0111111 0.675009 −1.247576 1000000 −0.752060 0.302196 1000001−0.788983 0.113122 1000010 −0.325356 0.054462 1000011 −0.573961 0.0989341000100 −0.579122 0.497202 1000101 −0.471776 0.396048 1000110 −0.2949170.133438 1000111 −0.433938 0.245088 1001000 −0.132847 0.742015 1001001−0.122253 0.604949 1001010 −0.068657 0.075472 1001011 −0.060983 0.4452071001100 −0.382346 0.652673 1001101 −0.302064 0.494450 1001110 −0.1664970.233502 1001111 −0.196116 0.340897 1010000 −0.907567 0.452354 1010001−1.043922 0.158157 1010010 −1.130081 0.548716 1010011 −1.320594 0.1814131010100 −0.712483 0.646623 1010101 −0.815526 0.865815 1010110 −1.1570760.928991 1010111 −1.532471 0.508968 1011000 −0.120519 0.915797 1011001−0.148259 1.123784 1011010 −0.282652 1.690100 1011011 −0.221465 1.3872361011100 −0.423824 0.821654 1011101 −0.488704 1.037583 1011110 −0.8725461.413810 1011111 −0.675009 1.247576 1100000 −0.752060 −0.302196 1100001−0.788983 −0.113122 1100010 −0.325356 −0.054462 1100011 −0.573961−0.098934 1100100 −0.579122 −0.497202 1100101 −0.471776 −0.3960481100110 −0.294917 −0.133438 1100111 −0.433938 −0.245088 1101000−0.132847 −0.742015 1101001 −0.122253 −0.604949 1101010 −0.068657−0.075472 1101011 −0.060983 −0.445207 1101100 −0.382346 −0.6526731101101 −0.302064 −0.494450 1101110 −0.166497 −0.233502 1101111−0.196116 −0.340897 1110000 −0.907567 −0.452354 1110001 −1.043922−0.158157 1110010 −1.130081 −0.548716 1110011 −1.320594 −0.1814131110100 −0.712483 −0.646623 1110101 −0.815526 −0.865815 1110110−1.157076 −0.928991 1110111 −1.532471 −0.508968 1111000 −0.120519−0.915797 1111001 −0.148259 −1.123784 1111010 −0.282652 −1.6901001111011 −0.221465 −1.387236 1111100 −0.423824 −0.821654 1111101−0.488704 −1.037583 1111110 −0.872546 −1.413810 1111111 −0.675009−1.247576

TABLE 21A SYMBOL COORDINATE BITS X Y 00000000 1.443706 0.533189 000000011.269957 0.814447 00000010 1.190815 0.494955 00000011 1.099458 0.63749300000100 1.465098 0.242389 00000101 0.756113 0.035702 00000110 1.7579590.251458 00000111 0.780617 0.113362 00001000 1.032269 1.540287 000010011.450983 1.025801 00001010 1.044843 0.407507 00001011 0.920903 0.47447100001100 1.061180 0.094137 00001101 0.942993 0.109431 00001110 1.1468650.181476 00001111 0.863666 0.236933 00010000 1.028531 1.046265 000100010.903477 0.907951 00010010 0.580224 0.575049 00010011 0.741607 0.72847100010100 0.418728 0.083169 00010101 0.537914 0.122315 00010110 0.5815230.384883 00010111 0.655016 0.231039 00011000 0.844978 1.282582 000110010.713419 0.974473 00011010 0.662139 0.570492 00011011 0.764324 0.61417200011100 0.401000 0.062964 00011101 0.510837 0.125696 00011110 0.5766090.374709 00011111 0.692682 0.292587 00100000 0.276792 1.794144 001000010.158046 1.018387 00100010 0.104813 0.702356 00100011 0.124613 0.88501600100100 0.110294 0.045410 00100101 0.068892 0.234221 00100110 0.1123440.534452 00100111 0.089452 0.398340 00101000 0.132300 1.285556 001010010.180106 1.107457 00101010 0.190850 0.723373 00101011 0.170166 0.86113700101100 0.088520 0.064328 00101101 0.063584 0.193067 00101110 0.1189190.539605 00101111 0.097923 0.408426 00110000 0.215811 1.558150 001100010.404454 1.021596 00110010 0.411119 0.597529 00110011 0.429107 0.83508900110100 0.269636 0.105598 00110101 0.260922 0.234821 00110110 0.3752580.455253 00110111 0.242072 0.352853 00111000 0.498501 1.328103 001110010.496854 1.034589 00111010 0.351667 0.652324 00111011 0.454845 0.85475800111100 0.278962 0.076488 00111101 0.267573 0.245109 00111110 0.3740770.452024 00111111 0.248176 0.363324 01000000 1.443706 −0.533189 010000011.269957 −0.814447 01000010 1.190815 −0.494955 01000011 1.099458−0.637493 01000100 1.465098 −0.242389 01000101 0.756113 −0.03570201000110 1.757959 −0.251458 01000111 0.780617 −0.113362 010010001.032269 −1.540287 01001001 1.450983 −1.025801 01001010 1.044843−0.407507 01001011 0.920903 −0.474471 01001100 1.061180 −0.09413701001101 0.942993 −0.109431 01001110 1.146865 −0.181476 010011110.863666 −0.236933 01010000 1.028531 −1.046265 01010001 0.903477−0.907951 01010010 0.580224 −0.575049 01010011 0.741607 −0.72847101010100 0.418728 −0.083169 01010101 0.537914 −0.122315 010101100.581523 −0.384883 01010111 0.655016 −0.231039 01011000 0.844978−1.282582 01011001 0.713419 −0.974473 01011010 0.662139 −0.57049201011011 0.764324 −0.614172 01011100 0.401000 −0.062964 010111010.510837 −0.125696 01011110 0.576609 −0.374709 01011111 0.692682−0.292587 01100000 0.276792 −1.794144 01100001 0.158046 −1.01838701100010 0.104813 −0.702356 01100011 0.124613 −0.885016 011001000.110294 −0.045410 01100101 0.068892 −0.234221 01100110 0.112344−0.534452 01100111 0.089452 −0.398340 01101000 0.132300 −1.28555601101001 0.180106 −1.107457 01101010 0.190850 −0.723373 011010110.170166 −0.861137 01101100 0.088520 −0.064328 01101101 0.063584−0.193067 01101110 0.118919 −0.539605 01101111 0.097923 −0.40842601110000 0.215811 −1.558150 01110001 0.404454 −1.021596 011100100.411119 −0.597529 01110011 0.429107 −0.835089 01110100 0.269636−0.105598 01110101 0.260922 −0.234821 01110110 0.375258 −0.45525301110111 0.242072 −0.352853 01111000 0.498501 −1.328103 011110010.496854 −1.034589 01111010 0.351667 −0.652324 01111011 0.454845−0.854758 01111100 0.278962 −0.076488 01111101 0.267573 −0.24510901111110 0.374077 −0.452024 01111111 0.248176 −0.363324 10000000−1.443706 0.533189 10000001 −1.269957 0.814447 10000010 −1.1908150.494955 10000011 −1.099458 0.637493 10000100 −1.465098 0.24238910000101 −0.756113 0.035702 10000110 −1.757959 0.251458 10000111−0.780617 0.113362 10001000 −1.032269 1.540287 10001001 −1.4509831.025801 10001010 −1.044843 0.407507 10001011 −0.920903 0.47447110001100 −1.061180 0.094137 10001101 −0.942993 0.109431 10001110−1.146865 0.181476 10001111 −0.863666 0.236933 10010000 −1.0285311.046265 10010001 −0.903477 0.907951 10010010 −0.580224 0.57504910010011 −0.741607 0.728471 10010100 −0.418728 0.083169 10010101−0.537914 0.122315 10010110 −0.581523 0.384883 10010111 −0.6550160.231039 10011000 −0.844978 1.282582 10011001 −0.713419 0.97447310011010 −0.662139 0.570492 10011011 −0.764324 0.614172 10011100−0.401000 0.062964 10011101 −0.510837 0.125696 10011110 −0.5766090.374709 10011111 −0.692682 0.292587 10100000 −0.276792 1.79414410100001 −0.158046 1.018387 10100010 −0.104813 0.702356 10100011−0.124613 0.885016 10100100 −0.110294 0.045410 10100101 −0.0688920.234221 10100110 −0.112344 0.534452 10100111 −0.089452 0.39834010101000 −0.132300 1.285556 10101001 −0.180106 1.107457 10101010−0.190850 0.723373 10101011 −0.170166 0.861137 10101100 −0.0885200.064328 10101101 −0.063584 0.193067 10101110 −0.118919 0.53960510101111 −0.097923 0.408426 10110000 −0.215811 1.558150 10110001−0.404454 1.021596 10110010 −0.411119 0.597529 10110011 −0.4291070.835089 10110100 −0.269636 0.105598 10110101 −0.260922 0.23482110110110 −0.375258 0.455253 10110111 −0.242072 0.352853 10111000−0.498501 1.328103 10111001 −0.496854 1.034589 10111010 −0.3516670.652324 10111011 −0.454845 0.854758 10111100 −0.278962 0.07648810111101 −0.267573 0.245109 10111110 −0.374077 0.452024 10111111−0.248176 0.363324 11000000 −1.443706 −0.533189 11000001 −1.269957−0.814447 11000010 −1.190815 −0.494955 11000011 −1.099458 −0.63749311000100 −1.465098 −0.242389 11000101 −0.756113 −0.035702 11000110−1.757959 −0.251458 11000111 −0.780617 −0.113362 11001000 −1.032269−1.540287 11001001 −1.450983 −1.025801 11001010 −1.044843 −0.40750711001011 −0.920903 −0.474471 11001100 −1.061180 −0.094137 11001101−0.942993 −0.109431 11001110 −1.146865 −0.181476 11001111 −0.863666−0.236933 11010000 −1.028531 −1.046265 11010001 −0.903477 −0.90795111010010 −0.580224 −0.575049 11010011 −0.741607 −0.728471 11010100−0.418728 −0.083169 11010101 −0.537914 −0.122315 11010110 −0.581523−0.384883 11010111 −0.655016 −0.231039 11011000 −0.844978 −1.28258211011001 −0.713419 −0.974473 11011010 −0.662139 −0.570492 11011011−0.764324 −0.614172 11011100 −0.401000 −0.062964 11011101 −0.510837−0.125696 11011110 −0.576609 −0.374709 11011111 −0.692682 −0.29258711100000 −0.276792 −1.794144 11100001 −0.158046 −1.018387 11100010−0.104813 −0.702356 11100011 −0.124613 −0.885016 11100100 −0.110294−0.045410 11100101 −0.068892 −0.234221 11100110 −0.112344 −0.53445211100111 −0.089452 −0.398340 11101000 −0.132300 −1.285556 11101001−0.180106 −1.107457 11101010 −0.190850 −0.723373 11101011 −0.170166−0.861137 11101100 −0.088520 −0.064328 11101101 −0.063584 −0.19306711101110 −0.118919 −0.539605 11101111 −0.097923 −0.408426 11110000−0.215811 −1.558150 11110001 −0.404454 −1.021596 11110010 −0.411119−0.597529 11110011 −0.429107 −0.835089 11110100 −0.269636 −0.10559811110101 −0.260922 −0.234821 11110110 −0.375258 −0.455253 11110111−0.242072 −0.352853 11111000 −0.498501 −1.328103 11111001 −0.496854−1.034589 11111010 −0.351667 −0.652324 11111011 −0.454845 −0.85475811111100 −0.278962 −0.076488 11111101 −0.267573 −0.245109 11111110−0.374077 −0.452024 11111111 −0.248176 −0.363324

TABLE 21B SYMBOL COORDINATE BITS X Y 00000000 0.975369 1.374032 000000011.481139 0.719889 00000010 1.218020 0.537432 00000011 1.572273 1.01357400000100 1.187472 0.140021 00000101 1.528894 0.437163 00000110 1.2094280.325388 00000111 1.451803 0.133447 00001000 1.150324 0.991883 000010010.920560 1.027887 00001010 1.130859 0.690274 00001011 0.935148 0.79109400001100 1.046905 0.109020 00001101 0.905564 0.126090 00001110 0.9868450.392801 00001111 0.888567 0.278893 00010000 0.311973 1.734362 000100010.529664 1.037246 00010010 0.623019 0.619800 00010011 0.545408 0.79451700010100 0.590997 0.100302 00010101 0.593410 0.246925 00010110 0.6071520.477790 00010111 0.629036 0.343531 00011000 0.563423 1.365187 000110010.710907 1.103897 00011010 0.763953 0.637666 00011011 0.728679 0.83790100011100 0.699119 0.052387 00011101 0.778520 0.167574 00011110 0.8411390.487476 00011111 0.768298 0.365852 00100000 0.127333 1.155716 001000010.307801 1.071269 00100010 0.054226 0.569000 00100011 0.045338 0.68181100100100 0.028860 0.067281 00100101 0.073608 0.181658 00100110 0.0368200.425876 00100111 0.052368 0.277893 00101000 0.043419 0.999378 001010010.134293 0.871130 00101010 0.167741 0.582866 00101011 0.144323 0.74586900101100 0.216884 0.055250 00101101 0.186854 0.164842 00101110 0.1606980.411437 00101111 0.184735 0.310456 00110000 0.173083 1.310422 001100010.373110 0.990945 00110010 0.442036 0.572513 00110011 0.450171 0.76199200110100 0.448273 0.078434 00110101 0.429733 0.223957 00110110 0.4335250.483009 00110111 0.442487 0.351997 00111000 0.234057 1.493126 001110010.245349 0.871117 00111010 0.278032 0.601780 00111011 0.299117 0.75256600111100 0.343828 0.049983 00111101 0.307660 0.197631 00111110 0.2568880.459299 00111111 0.301477 0.340566 01000000 0.975369 −1.374032 010000011.481139 −0.719889 01000010 1.218020 −0.537432 01000011 1.572273−1.013574 01000100 1.187472 −0.140021 01000101 1.528894 −0.43716301000110 1.209428 −0.325388 01000111 1.451803 −0.133447 010010001.150324 −0.991883 01001001 0.920560 −1.027887 01001010 1.130859−0.690274 01001011 0.935148 −0.791094 01001100 1.046905 −0.10902001001101 0.905564 −0.126090 01001110 0.986845 −0.392801 010011110.888567 −0.278893 01010000 0.311973 −1.734362 01010001 0.529664−1.037246 01010010 0.623019 −0.619800 01010011 0.545408 −0.79451701010100 0.590997 −0.100302 01010101 0.593410 −0.246925 010101100.607152 −0.477790 01010111 0.629036 −0.343531 01011000 0.563423−1.365187 01011001 0.710907 −1.103897 01011010 0.763953 −0.63766601011011 0.728679 −0.837901 01011100 0.699119 −0.052387 010111010.778520 −0.167574 01011110 0.841139 −0.487476 01011111 0.768298−0.365852 01100000 0.127333 −1.155716 01100001 0.307801 −1.07126901100010 0.054226 −0.569000 01100011 0.045338 −0.681811 011001000.028860 −0.067281 01100101 0.073608 −0.181658 01100110 0.036820−0.425876 01100111 0.052368 −0.277893 01101000 0.043419 −0.99937801101001 0.134293 −0.871130 01101010 0.167741 −0.582866 011010110.144323 −0.745869 01101100 0.216884 −0.055250 01101101 0.186854−0.164842 01101110 0.160698 −0.411437 01101111 0.184735 −0.31045601110000 0.173083 −1.310422 01110001 0.373110 −0.990945 011100100.442036 −0.572513 01110011 0.450171 −0.761992 01110100 0.448273−0.078434 01110101 0.429733 −0.223957 01110110 0.433525 −0.48300901110111 0.442487 −0.351997 01111000 0.234057 −1.493126 011110010.245349 −0.871117 01111010 0.278032 −0.601780 01111011 0.299117−0.752566 01111100 0.343828 −0.049983 01111101 0.307660 −0.19763101111110 0.256888 −0.459299 01111111 0.301477 −0.340566 10000000−0.975369 1.374032 10000001 −1.481139 0.719889 10000010 −1.2180200.537432 10000011 −1.572273 1.013574 10000100 −1.187472 0.14002110000101 −1.528894 0.437163 10000110 −1.209428 0.325388 10000111−1.451803 0.133447 10001000 −1.150324 0.991883 10001001 −0.9205601.027887 10001010 −1.130859 0.690274 10001011 −0.935148 0.79109410001100 −1.046905 0.109020 10001101 −0.905564 0.126090 10001110−0.986845 0.392801 10001111 −0.888567 0.278893 10010000 −0.3119731.734362 10010001 −0.529664 1.037246 10010010 −0.623019 0.61980010010011 −0.545408 0.794517 10010100 −0.590997 0.100302 10010101−0.593410 0.246925 10010110 −0.607152 0.477790 10010111 −0.6290360.343531 10011000 −0.563423 1.365187 10011001 −0.710907 1.10389710011010 −0.763953 0.637666 10011011 −0.728679 0.837901 10011100−0.699119 0.052387 10011101 −0.778520 0.167574 10011110 −0.8411390.487476 10011111 −0.768298 0.365852 10100000 −0.127333 1.15571610100001 −0.307801 1.071269 10100010 −0.054226 0.569000 10100011−0.045338 0.681811 10100100 −0.028860 0.067281 10100101 −0.0736080.181658 10100110 −0.036820 0.425876 10100111 −0.052368 0.27789310101000 −0.043419 0.999378 10101001 −0.134293 0.871130 10101010−0.167741 0.582866 10101011 −0.144323 0.745869 10101100 −0.2168840.055250 10101101 −0.186854 0.164842 10101110 −0.160698 0.41143710101111 −0.184735 0.310456 10110000 −0.173083 1.310422 10110001−0.373110 0.990945 10110010 −0.442036 0.572513 10110011 −0.4501710.761992 10110100 −0.448273 0.078434 10110101 −0.429733 0.22395710110110 −0.433525 0.483009 10110111 −0.442487 0.351997 10111000−0.234057 1.493126 10111001 −0.245349 0.871117 10111010 −0.2780320.601780 10111011 −0.299117 0.752566 10111100 −0.343828 0.04998310111101 −0.307660 0.197631 10111110 −0.256888 0.459299 10111111−0.301477 0.340566 11000000 −0.975369 −1.374032 11000001 −1.481139−0.719889 11000010 −1.218020 −0.537432 11000011 −1.572273 −1.01357411000100 −1.187472 −0.140021 11000101 −1.528894 −0.437163 11000110−1.209428 −0.325388 11000111 −1.451803 −0.133447 11001000 −1.150324−0.991883 11001001 −0.920560 −1.027887 11001010 −1.130859 −0.69027411001011 −0.935148 −0.791094 11001100 −1.046905 −0.109020 11001101−0.905564 −0.126090 11001110 −0.986845 −0.392801 11001111 −0.888567−0.278893 11010000 −0.311973 −1.734362 11010001 −0.529664 −1.03724611010010 −0.623019 −0.619800 11010011 −0.545408 −0.794517 11010100−0.590997 −0.100302 11010101 −0.593410 −0.246925 11010110 −0.607152−0.477790 11010111 −0.629036 −0.343531 11011000 −0.563423 −1.36518711011001 −0.710907 −1.103897 11011010 −0.763953 −0.637666 11011011−0.728679 −0.837901 11011100 −0.699119 −0.052387 11011101 −0.778520−0.167574 11011110 −0.841139 −0.487476 11011111 −0.768298 −0.36585211100000 −0.127333 −1.155716 11100001 −0.307801 −1.071269 11100010−0.054226 −0.569000 11100011 −0.045338 −0.681811 11100100 −0.028860−0.067281 11100101 −0.073608 −0.181658 11100110 −0.036820 −0.42587611100111 −0.052368 −0.277893 11101000 −0.043419 −0.999378 11101001−0.134293 −0.871130 11101010 −0.167741 −0.582866 11101011 −0.144323−0.745869 11101100 −0.216884 −0.055250 11101101 −0.186854 −0.16484211101110 −0.160698 −0.411437 11101111 −0.184735 −0.310456 11110000−0.173083 −1.310422 11110001 −0.373110 −0.990945 11110010 −0.442036−0.572513 11110011 −0.450171 −0.761992 11110100 −0.448273 −0.07843411110101 −0.429733 −0.223957 11110110 −0.433525 −0.483009 11110111−0.442487 −0.351997 11111000 −0.234057 −1.493126 11111001 −0.245349−0.871117 11111010 −0.278032 −0.601780 11111011 −0.299117 −0.75256611111100 −0.343828 −0.049983 11111101 −0.307660 −0.197631 11111110−0.256888 −0.459299 11111111 −0.301477 −0.340566

TABLE 21C SYMBOL COORDINATE BITS X Y 00000000 1.305348 0.483686 000000011.385995 0.667682 00000010 1.079272 0.658809 00000011 0.952913 0.61261400000100 1.407955 0.162208 00000101 0.743036 0.093077 00000110 1.6645440.277796 00000111 0.700449 0.240646 00001000 1.057746 1.546204 000010011.364655 0.938592 00001010 1.159648 0.316961 00001011 0.982972 0.39215700001100 0.953812 0.086185 00001101 0.865433 0.202042 00001110 1.1257990.109188 00001111 0.884989 0.377701 00010000 0.998762 0.983475 000100010.752453 0.974676 00010010 0.441612 0.542222 00010011 0.762558 0.77461300010100 0.542471 0.050180 00010101 0.566038 0.143317 00010110 0.5401930.413002 00010111 0.564199 0.285899 00011000 0.861634 1.190812 000110010.496817 1.189830 00011010 0.530301 0.608420 00011011 0.692344 0.63826300011100 0.415573 0.053395 00011101 0.452110 0.157963 00011110 0.6132130.496838 00011111 0.742823 0.455828 00100000 0.299991 1.828537 001000010.234715 1.027308 00100010 0.101242 0.654205 00100011 0.216049 0.94045800100100 0.149232 0.065752 00100101 0.079653 0.216567 00100110 0.1031540.579257 00100111 0.075918 0.328242 00101000 0.253926 1.421727 001010010.068626 1.125115 00101010 0.102520 0.767709 00101011 0.074965 0.88498000101100 0.075988 0.053940 00101101 0.026120 0.146113 00101110 0.0896990.491963 00101111 0.071658 0.412884 00110000 0.292967 1.624754 001100010.492228 1.002755 00110010 0.286607 0.646480 00110011 0.503324 0.86630000110100 0.230317 0.127990 00110101 0.244364 0.221890 00110110 0.2522360.527795 00110111 0.199080 0.311608 00111000 0.838132 1.415418 001110010.163432 1.243384 00111010 0.321389 0.731153 00111011 0.426149 0.80268700111100 0.302291 0.076239 00111101 0.350515 0.224507 00111110 0.3112650.430253 00111111 0.333302 0.349304 01000000 1.305348 −0.483686 010000011.385995 −0.667682 01000010 1.079272 −0.658809 01000011 0.952913−0.612614 01000100 1.407955 −0.162208 01000101 0.743036 −0.09307701000110 1.664544 −0.277796 01000111 0.700449 −0.240646 010010001.057746 −1.546204 01001001 1.364655 −0.938592 01001010 1.159648−0.316961 01001011 0.982972 −0.392157 01001100 0.953812 −0.08618501001101 0.865433 −0.202042 01001110 1.125799 −0.109188 010011110.884989 −0.377701 01010000 0.998762 −0.983475 01010001 0.752453−0.974676 01010010 0.441612 −0.542222 01010011 0.762558 −0.77461301010100 0.542471 −0.050180 01010101 0.566038 −0.143317 010101100.540193 −0.413002 01010111 0.564199 −0.285899 01011000 0.861634−1.190812 01011001 0.496817 −1.189830 01011010 0.530301 −0.60842001011011 0.692344 −0.638263 01011100 0.415573 −0.053395 010111010.452110 −0.157963 01011110 0.613213 −0.496838 01011111 0.742823−0.455828 01100000 0.299991 −1.828537 01100001 0.234715 −1.02730801100010 0.101242 −0.654205 01100011 0.216049 −0.940458 011001000.149232 −0.065752 01100101 0.079653 −0.216567 01100110 0.103154−0.579257 01100111 0.075918 −0.328242 01101000 0.253926 −1.42172701101001 0.068626 −1.125115 01101010 0.102520 −0.767709 011010110.074965 −0.884980 01101100 0.075988 −0.053940 01101101 0.026120−0.146113 01101110 0.089699 −0.491963 01101111 0.071658 −0.41288401110000 0.292967 −1.624754 01110001 0.492228 −1.002755 011100100.286607 −0.646480 01110011 0.503324 −0.866300 01110100 0.230317−0.127990 01110101 0.244364 −0.221890 01110110 0.252236 −0.52779501110111 0.199080 −0.311608 01111000 0.838132 −1.415418 011110010.163432 −1.243384 01111010 0.321389 −0.731153 01111011 0.426149−0.802687 01111100 0.302291 −0.076239 01111101 0.350515 −0.22450701111110 0.311265 −0.430253 01111111 0.333302 −0.349304 10000000−1.305348 0.483686 10000001 −1.385995 0.667682 10000010 −1.0792720.658809 10000011 −0.952913 0.612614 10000100 −1.407955 0.16220810000101 −0.743036 0.093077 10000110 −1.664544 0.277796 10000111−0.700449 0.240646 10001000 −1.057746 1.546204 10001001 −1.3646550.938592 10001010 −1.159648 0.316961 10001011 −0.982972 0.39215710001100 −0.953812 0.086185 10001101 −0.865433 0.202042 10001110−1.125799 0.109188 10001111 −0.884989 0.377701 10010000 −0.9987620.983475 10010001 −0.752453 0.974676 10010010 −0.441612 0.54222210010011 −0.762558 0.774613 10010100 −0.542471 0.050180 10010101−0.566038 0.143317 10010110 −0.540193 0.413002 10010111 −0.5641990.285899 10011000 −0.861634 1.190812 10011001 −0.496817 1.18983010011010 −0.530301 0.608420 10011011 −0.692344 0.638263 10011100−0.415573 0.053395 10011101 −0.452110 0.157963 10011110 −0.6132130.496838 10011111 −0.742823 0.455828 10100000 −0.299991 1.82853710100001 −0.234715 1.027308 10100010 −0.101242 0.654205 10100011−0.216049 0.940458 10100100 −0.149232 0.065752 10100101 −0.0796530.216567 10100110 −0.103154 0.579257 10100111 −0.075918 0.32824210101000 −0.253926 1.421727 10101001 −0.068626 1.125115 10101010−0.102520 0.767709 10101011 −0.074965 0.884980 10101100 −0.0759880.053940 10101101 −0.026120 0.146113 10101110 −0.089699 0.49196310101111 −0.071658 0.412884 10110000 −0.292967 1.624754 10110001−0.492228 1.002755 10110010 −0.286607 0.646480 10110011 −0.5033240.866300 10110100 −0.230317 0.127990 10110101 −0.244364 0.22189010110110 −0.252236 0.527795 10110111 −0.199080 0.311608 10111000−0.838132 1.415418 10111001 −0.163432 1.243384 10111010 −0.3213890.731153 10111011 −0.426149 0.802687 10111100 −0.302291 0.07623910111101 −0.350515 0.224507 10111110 −0.311265 0.430253 10111111−0.333302 0.349304 11000000 −1.305348 −0.483686 11000001 −1.385995−0.667682 11000010 −1.079272 −0.658809 11000011 −0.952913 −0.61261411000100 −1.407955 −0.162208 11000101 −0.743036 −0.093077 11000110−1.664544 −0.277796 11000111 −0.700449 −0.240646 11001000 −1.057746−1.546204 11001001 −1.364655 −0.938592 11001010 −1.159648 −0.31696111001011 −0.982972 −0.392157 11001100 −0.953812 −0.086185 11001101−0.865433 −0.202042 11001110 −1.125799 −0.109188 11001111 −0.884989−0.377701 11010000 −0.998762 −0.983475 11010001 −0.752453 −0.97467611010010 −0.441612 −0.542222 11010011 −0.762558 −0.774613 11010100−0.542471 −0.050180 11010101 −0.566038 −0.143317 11010110 −0.540193−0.413002 11010111 −0.564199 −0.285899 11011000 −0.861634 −1.19081211011001 −0.496817 −1.189830 11011010 −0.530301 −0.608420 11011011−0.692344 −0.638263 11011100 −0.415573 −0.053395 11011101 −0.452110−0.157963 11011110 −0.613213 −0.496838 11011111 −0.742823 −0.45582811100000 −0.299991 −1.828537 11100001 −0.234715 −1.027308 11100010−0.101242 −0.654205 11100011 −0.216049 −0.940458 11100100 −0.149232−0.065752 11100101 −0.079653 −0.216567 11100110 −0.103154 −0.57925711100111 −0.075918 −0.328242 11101000 −0.253926 −1.421727 11101001−0.068626 −1.125115 11101010 −0.102520 −0.767709 11101011 −0.074965−0.884980 11101100 −0.075988 −0.053940 11101101 −0.026120 −0.14611311101110 −0.089699 −0.491963 11101111 −0.071658 −0.412884 11110000−0.292967 −1.624754 11110001 −0.492228 −1.002755 11110010 −0.286607−0.646480 11110011 −0.503324 −0.866300 11110100 −0.230317 −0.12799011110101 −0.244364 −0.221890 11110110 −0.252236 −0.527795 11110111−0.199080 −0.311608 11111000 −0.838132 −1.415418 11111001 −0.163432−1.243384 11111010 −0.321389 −0.731153 11111011 −0.426149 −0.80268711111100 −0.302291 −0.076239 11111101 −0.350515 −0.224507 11111110−0.311265 −0.430253 11111111 −0.333302 −0.349304

TABLE 22 SYMBOL COORDINATE BITS X Y 0000 0.270682 0.962663 0001 0.2535730.248544 0010 0.707302 0.706911 0011 0.961176 0.275819 0100 0.270682−0.962663 0101 0.253573 −0.248544 0110 0.707302 −0.706911 0111 0.961176−0.275819 1000 −0.270682 0.962663 1001 −0.253573 0.248544 1010 −0.7073020.706911 1011 −0.961176 0.275819 1100 −0.270682 −0.962663 1101 −0.253573−0.248544 1110 −0.707302 −0.706911 1111 −0.961176 −0.275819

TABLE 23 SYMBOL COORDINATE BITS X Y 00000 0.358210 0.139403 000010.235261 0.421763 00010 0.930790 0.364753 00011 0.787656 0.614713 001000.125482 0.991921 00101 0.382784 0.922993 00110 0.990631 0.136566 001110.626638 0.778830 01000 0.358210 −0.139403 01001 0.235261 −0.42176301010 0.930790 −0.364753 01011 0.787656 −0.614713 01100 0.125482−0.991921 01101 0.382784 −0.922993 01110 0.990631 −0.136566 011110.626638 −0.778830 10000 −0.358210 0.139403 10001 −0.235261 0.42176310010 −0.930790 0.364753 10011 −0.787656 0.614713 10100 −0.1254820.991921 10101 −0.382784 0.922993 10110 −0.990631 0.136566 10111−0.626638 0.778830 11000 −0.358210 −0.139403 11001 −0.235261 −0.42176311010 −0.930790 −0.364753 11011 −0.787656 −0.614713 11100 −0.125482−0.991921 11101 −0.382784 −0.922993 11110 −0.990631 −0.136566 11111−0.626638 −0.778830

TABLE 24A SYMBOL COORDINATE BITS X Y 000000 0.894480 0.445822 0000010.890395 0.455110 000010 0.984821 0.172554 000011 0.985411 0.170142000100 0.730858 0.679601 000101 0.731787 0.681533 000110 0.5943650.254018 000111 0.545682 0.183541 001000 0.172908 0.983278 0010010.144365 0.988438 001010 0.103984 0.512065 001011 0.110135 0.138733001100 0.453133 0.891044 001101 0.458751 0.888174 001110 0.2379030.413635 001111 0.327635 0.213996 010000 0.894480 −0.445822 0100010.890395 −0.455110 010010 0.984821 −0.172554 010011 0.985411 −0.170142010100 0.730858 −0.679601 010101 0.731787 −0.681533 010110 0.594365−0.254018 010111 0.545682 −0.183541 011000 0.172908 −0.983278 0110010.144365 −0.988438 011010 0.103984 −0.512065 011011 0.110135 −0.138733011100 0.453133 −0.891044 011101 0.458751 −0.888174 011110 0.237903−0.413635 011111 0.327635 −0.213996 100000 −0.894480 0.445822 100001−0.890395 0.455110 100010 −0.984821 0.172554 100011 −0.985411 0.170142100100 −0.730858 0.679601 100101 −0.731787 0.681533 100110 −0.5943650.254018 100111 −0.545682 0.183541 101000 −0.172908 0.983278 101001−0.144365 0.988438 101010 −0.103984 0.512065 101011 −0.110135 0.138733101100 −0.453133 0.891044 101101 −0.458751 0.888174 101110 −0.2379030.413635 101111 −0.327635 0.213996 110000 −0.894480 −0.445822 110001−0.890395 −0.455110 110100 −0.984821 −0.172554 110011 −0.985411−0.170142 110100 −0.730858 −0.679601 110101 −0.731787 −0.681533 110110−0.594365 −0.254018 110111 −0.545682 −0.183541 111000 −0.172908−0.983278 111001 −0.144365 −0.988438 111010 −0.103984 −0.512065 111011−0.110135 −0.138733 111100 −0.453133 −0.891044 111101 −0.458751−0.888174 111110 −0.237903 −0.413635 111111 −0.327635 −0.213996

TABLE 24B SYMBOL COORDINATE BITS X Y 000000 0.847425 0.528328 0000010.724032 0.689761 000010 0.949712 0.313126 000011 0.993100 0.116019000100 0.561795 0.514360 000101 0.575688 0.817191 000110 0.5866610.291101 000111 0.623692 0.093506 001000 0.114854 0.716644 0010010.141761 0.989893 001010 0.099426 0.429732 001011 0.092178 0.159156001100 0.344522 0.588449 001101 0.385307 0.921869 001110 0.3144410.342702 001111 0.309723 0.111529 010000 0.847425 −0.528328 0100010.724032 −0.689761 010010 0.949712 −0.313126 010011 0.993100 −0.116019010100 0.561795 −0.514360 010101 0.575688 −0.817191 010110 0.586661−0.291101 010111 0.623692 −0.093506 011000 0.114854 −0.716644 0110010.141761 −0.989893 011010 0.099426 −0.429732 011011 0.092178 −0.159156011100 0.344522 −0.588449 011101 0.385307 −0.921869 011110 0.314441−0.342702 011111 0.309723 −0.111529 100000 −0.847425 0.528328 100001−0.724032 0.689761 100010 −0.949712 0.313126 100011 −0.993100 0.116019100100 −0.561795 0.514360 100101 −0.575688 0.817191 100110 −0.5866610.291101 100111 −0.623692 0.093506 101000 −0.114854 0.716644 101001−0.141761 0.989893 101010 −0.099426 0.429732 101011 −0.092178 0.159156101100 −0.344522 0.588449 101101 −0.385307 0.921869 101110 −0.3144410.342702 101111 −0.309723 0.111529 110000 −0.847425 −0.528328 110001−0.724032 −0.689761 110010 −0.949712 −0.313126 110011 −0.993100−0.116019 110100 −0.561795 −0.514360 110101 −0.575688 −0.817191 110110−0.586661 −0.291101 110111 −0.623692 −0.093506 111000 −0.114854−0.716644 111001 −0.141761 −0.989893 111010 −0.099426 −0.429732 111011−0.092178 −0.159156 111100 −0.344522 −0.588449 111101 −0.385307−0.921869 111110 −0.314441 −0.342702 111111 −0.309723 −0.111529

TABLE 24C SYMBOL COORDINATE BITS X Y 000000 0.089757 0.995927 0000010.871842 0.489415 000010 0.992114 0.111242 000011 0.947926 0.318276000100 0.624995 0.779546 000101 0.766239 0.642268 000110 0.6310560.095979 000111 0.627559 0.304108 001000 0.276549 0.960689 0010010.111329 0.622856 001010 0.150023 0.138919 001011 0.116201 0.363483001100 0.453255 0.891381 001101 0.390500 0.599215 001110 0.3324230.100418 001111 0.436529 0.401382 010000 0.089757 −0.995927 0100010.871842 −0.489415 010010 0.992114 −0.111242 010011 0.947926 −0.318276010100 0.624995 −0.779546 010101 0.766239 −0.642268 010110 0.631056−0.095979 010111 0.627559 −0.304108 011000 0.276549 −0.960689 0110010.111329 −0.622856 011010 0.150023 −0.138919 011011 0.116201 −0.363483011100 0.453255 −0.891381 011101 0.390500 −0.599215 011110 0.332423−0.100418 011111 0.436529 −0.401382 100000 −0.089757 0.995927 100001−0.871842 0.489415 100010 −0.992114 0.111242 100011 −0.947926 0.318276100100 −0.624995 0.779546 100101 −0.766239 0.642268 100110 −0.6310560.095979 100111 −0.627559 0.304108 101000 −0.276549 0.960689 101001−0.111329 0.622856 101010 −0.150023 0.138919 101011 −0.116201 0.363483101100 −0.453255 0.891381 101101 −0.390500 0.599215 101110 −0.3324230.100418 101111 −0.436529 0.401382 110000 −0.089757 −0.995927 110001−0.871842 −0.489415 110010 −0.992114 −0.111242 110011 −0.947926−0.318276 110100 −0.624995 −0.779546 110101 −0.766239 −0.642268 110110−0.631056 −0.095979 110111 −0.627559 −0.304108 111000 −0.276549−0.960689 111001 −0.111329 −0.622856 111010 −0.150023 −0.138919 111011−0.116201 −0.363483 111100 −0.453255 −0.891381 111101 −0.390500−0.599215 111110 −0.332423 −0.100418 111111 −0.436529 −0.401382

TABLE 24D SYMBOL COORDINATE BITS X Y 000000 0.825394 0.564557 0000010.679474 0.733233 000010 0.934649 0.354296 000011 0.992113 0.124306000100 0.547499 0.538212 000101 0.512966 0.857155 000110 0.6678740.319131 000111 0.704023 0.112315 001000 0.105064 0.673007 0010010.104623 0.989353 001010 0.128136 0.390102 001011 0.131864 0.120209001100 0.337537 0.644600 001101 0.310475 0.949750 001110 0.3643370.376712 001111 0.404674 0.115168 010000 0.825394 −0.564557 0100010.679474 −0.733233 010010 0.934649 −0.354296 010011 0.992113 −0.124306010100 0.547499 −0.538212 010101 0.512966 −0.857155 010110 0.667874−0.319131 010111 0.704023 −0.112315 011000 0.105064 −0.673007 0110010.104623 −0.989353 011010 0.128136 −0.390102 011011 0.131864 −0.120209011100 0.337537 −0.644600 011101 0.310475 −0.949750 011110 0.364337−0.376712 011111 0.404674 −0.115168 100000 −0.825394 0.564557 100001−0.679474 0.733233 100010 −0.934649 0.354296 100011 −0.992113 0.124306100100 −0.547499 0.538212 100101 −0.512966 0.857155 100110 −0.6678740.319131 100111 −0.704023 0.112315 101000 −0.105064 0.673007 101001−0.104623 0.989353 101010 −0.128136 0.390102 101011 −0.131864 0.120209101100 −0.337537 0.644600 101101 −0.310475 0.949750 101110 −0.3643370.376712 101111 −0.404674 0.115168 110000 −0.825394 −0.564557 110001−0.679474 −0.733233 110010 −0.934649 −0.354296 110011 −0.992113−0.124306 110100 −0.547499 −0.538212 110101 −0.512966 −0.857155 110110−0.667874 −0.319131 110111 −0.704023 −0.112315 111000 −0.105064−0.673007 111001 −0.104623 −0.989353 111010 −0.128136 −0.390102 111011−0.131864 −0.120209 111100 −0.337537 −0.644600 111101 −0.310475−0.949750 111110 −0.364337 −0.376712 111111 −0.404674 −0.115168

TABLE 25A SYMBOL COORDINATE BITS X Y 0000000 0.401618 0.182455 00000010.432271 0.238332 0000010 0.210211 0.077897 0000011 0.188527 0.1061440000100 0.690013 0.077217 0000101 0.658899 0.105155 0000110 0.9917920.108289 0000111 0.994471 0.097881 0001000 0.266643 0.496767 00010010.335273 0.407525 0001010 0.087396 0.426683 0001011 0.081485 0.2855450001100 0.157416 0.730291 0001101 0.144214 0.989148 0001110 0.0755480.683943 0001111 0.123780 0.992051 0010000 0.632012 0.419775 00100010.581779 0.400034 0010010 0.818321 0.574028 0010011 0.808932 0.5857100010100 0.772679 0.293599 0010101 0.753516 0.255345 0010110 0.9370560.349179 0010111 0.937889 0.344474 0011000 0.484355 0.600452 00110010.469372 0.569456 0011010 0.650758 0.755708 0011011 0.663597 0.7437860011100 0.362030 0.806477 0011101 0.324343 0.942537 0011110 0.4578170.888570 0011111 0.394670 0.918198 0100000 0.401618 −0.182455 01000010.432271 −0.238332 0100010 0.210211 −0.077897 0100011 0.188527 −0.1061440100100 0.690013 −0.077217 0100101 0.658899 −0.105155 0100110 0.991792−0.108289 0100111 0.994471 −0.097881 0101000 0.266643 −0.496767 01010010.335273 −0.407525 0101010 0.087396 −0.426683 0101011 0.081485 −0.2855450101100 0.157416 −0.730291 0101101 0.144214 −0.989148 0101110 0.075548−0.683943 0101111 0.123780 −0.992051 0110000 0.632012 −0.419775 01100010.581779 −0.400034 0110010 0.818321 −0.574028 0110011 0.808932 −0.5857100110100 0.772679 −0.293599 0110101 0.753516 −0.255345 0110110 0.937056−0.349179 0110111 0.937889 −0.344474 0111000 0.484355 −0.600452 01110010.469372 −0.569456 0111010 0.650758 −0.755708 0111011 0.663597 −0.7437860111100 0.362030 −0.806477 0111101 0.324343 −0.942537 0111110 0.457817−0.888570 0111111 0.394670 −0.918198 1000000 −0.401618 0.182455 1000001−0.432271 0.238332 1000010 −0.210211 0.077897 1000011 −0.188527 0.1061441000100 −0.690013 0.077217 1000101 −0.658899 0.105155 1000110 −0.9917920.108289 1000111 −0.994471 0.097881 1001000 −0.266643 0.496767 1001001−0.335273 0.407525 1001010 −0.087396 0.426683 1001011 −0.081485 0.2855451001100 −0.157416 0.730291 1001101 −0.144214 0.989148 1001110 −0.0755480.683943 1001111 −0.123780 0.992051 1010000 −0.632012 0.419775 1010001−0.581779 0.400034 1010010 −0.818321 0.574028 1010011 −0.808932 0.5857101010100 −0.772679 0.293599 1010101 −0.753516 0.255345 1010110 −0.9370560.349179 1010111 −0.937889 0.344474 1011000 −0.484355 0.600452 1011001−0.469372 0.569456 1011010 −0.650758 0.755708 1011011 −0.663597 0.7437861011100 −0.362030 0.806477 1011101 −0.324343 0.942537 1011110 −0.4578170.888570 1011111 −0.394670 0.918198 1100000 −0.401618 −0.182455 1100001−0.432271 −0.238332 1100010 −0.210211 −0.077897 1100011 −0.188527−0.106144 1100100 −0.690013 −0.077217 1100101 −0.658899 −0.1051551100110 −0.991792 −0.108289 1100111 −0.994471 −0.097881 1101000−0.266643 −0.496767 1101001 −0.335273 −0.407525 1101010 −0.087396−0.426683 1101011 −0.081485 −0.285545 1101100 −0.157416 −0.7302911101101 −0.144214 −0.989148 1101110 −0.075548 −0.683943 1101111−0.123780 −0.992051 1110000 −0.632012 −0.419775 1110001 −0.581779−0.400034 1110010 −0.818321 −0.574028 1110011 −0.808932 −0.5857101110100 −0.772679 −0.293599 1110101 −0.753516 −0.255345 1110110−0.937056 −0.349179 1110111 −0.937889 −0.344474 1111000 −0.484355−0.600452 1111001 −0.469372 −0.569456 1111010 −0.650758 −0.7557081111011 −0.663597 −0.743786 1111100 −0.362030 −0.806477 1111101−0.324343 −0.942537 1111110 −0.457817 −0.888570 1111111 −0.394670−0.918198

TABLE 25B SYMBOL COORDINATE BITS X Y 0000000 0.349139 0.084873 00000010.444253 0.223961 0000010 0.200465 0.076363 0000011 0.076729 0.1653910000100 0.661752 0.074430 0000101 0.569082 0.152245 0000110 0.8674630.058010 0000111 0.994165 0.101734 0001000 0.276140 0.483395 00010010.360395 0.354916 0001010 0.105450 0.423216 0001011 0.112712 0.3064080001100 0.157400 0.694676 0001101 0.092859 0.872214 0001110 0.0735730.584372 0001111 0.086593 0.996244 0010000 0.664424 0.454352 00100010.620132 0.459156 0010010 0.822650 0.566931 0010011 0.811832 0.5833710010100 0.734535 0.287119 0010101 0.698954 0.273938 0010110 0.9328160.357106 0010111 0.955383 0.292872 0011000 0.415243 0.605429 00110010.487527 0.551685 0011010 0.624474 0.780353 0011011 0.654058 0.7554200011100 0.291362 0.740066 0011101 0.280086 0.955742 0011110 0.4631770.885940 0011111 0.351608 0.935764 0100000 0.349139 −0.084873 01000010.444253 −0.223961 0100010 0.200465 −0.076363 0100011 0.076729 −0.1653910100100 0.661752 −0.074430 0100101 0.569082 −0.152245 0100110 0.867463−0.058010 0100111 0.994165 −0.101734 0101000 0.276140 −0.483395 01010010.360395 −0.354916 0101010 0.105450 −0.423216 0101011 0.112712 −0.3064080101100 0.157400 −0.694676 0101101 0.092859 −0.872214 0101110 0.073573−0.584372 0101111 0.086593 −0.996244 0110000 0.664424 −0.454352 01100010.620132 −0.459156 0110010 0.822650 −0.566931 0110011 0.811832 −0.5833710110100 0.734535 −0.287119 0110101 0.698954 −0.273938 0110110 0.932816−0.357106 0110111 0.955383 −0.292872 0111000 0.415243 −0.605429 01110010.487527 −0.551685 0111010 0.624474 −0.780353 0111011 0.654058 −0.7554200111100 0.291362 −0.740066 0111101 0.280086 −0.955742 0111110 0.463177−0.885940 0111111 0.351608 −0.935764 1000000 −0.349139 0.084873 1000001−0.444253 0.223961 1000010 −0.200465 0.076363 1000011 −0.076729 0.1653911000100 −0.661752 0.074430 1000101 −0.569082 0.152245 1000110 −0.8674630.058010 1000111 −0.994165 0.101734 1001000 −0.276140 0.483395 1001001−0.360395 0.354916 1001010 −0.105450 0.423216 1001011 −0.112712 0.3064081001100 −0.157400 0.694676 1001101 −0.092859 0.872214 1001110 −0.0735730.584372 1001111 −0.086593 0.996244 1010000 −0.664424 0.454352 1010001−0.620132 0.459156 1010010 −0.822650 0.566931 1010011 −0.811832 0.5833711010100 −0.734535 0.287119 1010101 −0.698954 0.273938 1010110 −0.9328160.357106 1010111 −0.955383 0.292872 1011000 −0.415243 0.605429 1011001−0.487527 0.551685 1011010 −0.624474 0.780353 1011011 −0.654058 0.7554201011100 −0.291362 0.740066 1011101 −0.280086 0.955742 1011110 −0.4631770.885940 1011111 −0.351608 0.935764 1100000 −0.349139 −0.084873 1100001−0.444253 −0.223961 1100010 −0.200465 −0.076363 1100011 −0.076729−0.165391 1100100 −0.661752 −0.074430 1100101 −0.569082 −0.1522451100110 −0.867463 −0.058010 1100111 −0.994165 −0.101734 1101000−0.276140 −0.483395 1101001 −0.360395 −0.354916 1101010 −0.105450−0.423216 1101011 −0.112712 −0.306408 1101100 −0.157400 −0.6946761101101 −0.092859 −0.872214 1101110 −0.073573 −0.584372 1101111−0.086593 −0.996244 1110000 −0.664424 −0.454352 1110001 −0.620132−0.459156 1110010 −0.822650 −0.566931 1110011 −0.811832 −0.5833711110100 −0.734535 −0.287119 1110101 −0.698954 −0.273938 1110110−0.932816 −0.357106 1110111 −0.955383 −0.292872 1111000 −0.415243−0.605429 1111001 −0.487527 −0.551685 1111010 −0.624474 −0.7803531111011 −0.654058 −0.755420 1111100 −0.291362 −0.740066 1111101−0.280086 −0.955742 1111110 −0.463177 −0.885940 1111111 −0.351608−0.935764

TABLE 25C SYMBOL COORDINATE BITS X Y 0000000 0.179332 0.062318 00000010.264529 0.196526 0000010 0.055320 0.109173 0000011 0.101863 0.2351720000100 0.669962 0.075558 0000101 0.419174 0.070925 0000110 0.8610920.104401 0000111 0.992390 0.118291 0001000 0.195476 0.575233 00010010.219531 0.412072 0001010 0.060970 0.560996 0001011 0.085387 0.3698040001100 0.213900 0.756034 0001101 0.279980 0.959448 0001110 0.0783560.804679 0001111 0.089502 0.994559 0010000 0.552393 0.333246 00100010.396346 0.273296 0010010 0.683752 0.404797 0010011 0.858560 0.5112640010100 0.642493 0.197800 0010101 0.462109 0.164180 0010110 0.8016940.290343 0010111 0.937916 0.339763 0011000 0.412951 0.509479 00110010.336567 0.413951 0011010 0.600289 0.546834 0011011 0.763765 0.6446260011100 0.385655 0.691063 0011101 0.443902 0.896057 0011110 0.5364730.674051 0011111 0.606478 0.795101 0100000 0.179332 −0.062318 01000010.264529 −0.196526 0100010 0.055320 −0.109173 0100011 0.101863 −0.2351720100100 0.669962 −0.075558 0100101 0.419174 −0.070925 0100110 0.861092−0.104401 0100111 0.992390 −0.118291 0101000 0.195476 −0.575233 01010010.219531 −0.412072 0101010 0.060970 −0.560996 0101011 0.085387 −0.3698040101100 0.213900 −0.756034 0101101 0.279980 −0.959448 0101110 0.078356−0.804679 0101111 0.089502 −0.994559 0110000 0.552393 −0.333246 01100010.396346 −0.273296 0110010 0.683752 −0.404797 0110011 0.858560 −0.5112640110100 0.642493 −0.197800 0110101 0.462109 −0.164180 0110110 0.801694−0.290343 0110111 0.937916 −0.339763 0111000 0.412951 −0.509479 01110010.336567 −0.413951 0111010 0.600289 −0.546834 0111011 0.763765 −0.6446260111100 0.385655 −0.691063 0111101 0.443902 −0.896057 0111110 0.536473−0.674051 0111111 0.606478 −0.795101 1000000 −0.179332 0.062318 1000001−0.264529 0.196526 1000010 −0.055320 0.109173 1000011 −0.101863 0.2351721000100 −0.669962 0.075558 1000101 −0.419174 0.070925 1000110 −0.8610920.104401 1000111 −0.992390 0.118291 1001000 −0.195476 0.575233 1001001−0.219531 0.412072 1001010 −0.060970 0.560996 1001011 −0.085387 0.3698041001100 −0.213900 0.756034 1001101 −0.279980 0.959448 1001110 −0.0783560.804679 1001111 −0.089502 0.994559 1010000 −0.552393 0.333246 1010001−0.396346 0.273296 1010010 −0.683752 0.404797 1010011 −0.858560 0.5112641010100 −0.642493 0.197800 1010101 −0.462109 0.164180 1010110 −0.8016940.290343 1010111 −0.937916 0.339763 1011000 −0.412951 0.509479 1011001−0.336567 0.413951 1011010 −0.600289 0.546834 1011011 −0.763765 0.6446261011100 −0.385655 0.691063 1011101 −0.443902 0.896057 1011110 −0.5364730.674051 1011111 −0.606478 0.795101 1100000 −0.179332 −0.062318 1100001−0.264529 −0.196526 1100010 −0.055320 −0.109173 1100011 −0.101863−0.235172 1100100 −0.669962 −0.075558 1100101 −0.419174 −0.0709251100110 −0.861092 −0.104401 1100111 −0.992390 −0.118291 1101000−0.195476 −0.575233 1101001 −0.219531 −0.412072 1101010 −0.060970−0.560996 1101011 −0.085387 −0.369804 1101100 −0.213900 −0.7560341101101 −0.279980 −0.959448 1101110 −0.078356 −0.804679 1101111−0.089502 −0.994559 1110000 −0.552393 −0.333246 1110001 −0.396346−0.273296 1110010 −0.683752 −0.404797 1110011 −0.858560 −0.5112641110100 −0.642493 −0.197800 1110101 −0.462109 −0.164180 1110110−0.801694 −0.290343 1110111 −0.937916 −0.339763 1111000 −0.412951−0.509479 1111001 −0.336567 −0.413951 1111010 −0.600289 −0.5468341111011 −0.763765 −0.644626 1111100 −0.385655 −0.691063 1111101−0.443902 −0.896057 1111110 −0.536473 −0.674051 1111111 −0.606478−0.795101

TABLE 25D SYMBOL COORDINATE BITS X Y 0000000 0.215659 0.071275 00000010.247193 0.239779 0000010 0.059723 0.089476 0000011 0.084352 0.2562860000100 0.631601 0.086959 0000101 0.421425 0.060957 0000110 0.8110360.081198 0000111 0.989141 0.115779 0001000 0.238961 0.619410 00010010.188755 0.432433 0001010 0.081970 0.619772 0001011 0.071916 0.4460110001100 0.230093 0.798693 0001101 0.278409 0.959192 0001110 0.0793760.797516 0001111 0.102980 0.994337 0010000 0.540893 0.373750 00100010.390688 0.300381 0010010 0.711286 0.403395 0010011 0.878402 0.4771310010100 0.613230 0.218230 0010101 0.459120 0.180142 0010110 0.7705400.249889 0010111 0.951364 0.303258 0011000 0.419831 0.530248 00110010.327094 0.416570 0011010 0.635577 0.561146 0011011 0.777941 0.6270400011100 0.406760 0.706463 0011101 0.454097 0.890952 0011110 0.5549360.677703 0011111 0.616155 0.785695 0100000 0.215659 −0.071275 01000010.247193 −0.239779 0100010 0.059723 −0.089476 0100011 0.084352 −0.2562860100100 0.631601 −0.086959 0100101 0.421425 −0.060957 0100110 0.811036−0.081198 0100111 0.989141 −0.115779 0101000 0.238961 −0.619410 01010010.188755 −0.432433 0101010 0.081970 −0.619772 0101011 0.071916 −0.4460110101100 0.230093 −0.798693 0101101 0.278409 −0.959192 0101110 0.079376−0.797516 0101111 0.102980 −0.994337 0110000 0.540893 −0.373750 01100010.390688 −0.300381 0110010 0.711286 −0.403395 0110011 0.878402 −0.4771310110100 0.613230 −0.218230 0110101 0.459120 −0.180142 0110110 0.770540−0.249889 0110111 0.951364 −0.303258 0111000 0.419831 −0.530248 01110010.327094 −0.416570 0111010 0.635577 −0.561146 0111011 0.777941 −0.6270400111100 0.406760 −0.706463 0111101 0.454097 −0.890952 0111110 0.554936−0.677703 0111111 0.616155 −0.785695 1000000 −0.215659 0.071275 1000001−0.247193 0.239779 1000010 −0.059723 0.089476 1000011 −0.084352 0.2562861000100 −0.631601 0.086959 1000101 −0.421425 0.060957 1000110 −0.8110360.081198 1000111 −0.989141 0.115779 1001000 −0.238961 0.619410 1001001−0.188755 0.432433 1001010 −0.081970 0.619772 1001011 −0.071916 0.4460111001100 −0.230093 0.798693 1001101 −0.278409 0.959192 1001110 −0.0793760.797516 1001111 −0.102980 0.994337 1010000 −0.540893 0.373750 1010001−0.390688 0.300381 1010010 −0.711286 0.403395 1010011 −0.878402 0.4771311010100 −0.613230 0.218230 1010101 −0.459120 0.180142 1010110 −0.7705400.249889 1010111 −0.951364 0.303258 1011000 −0.419831 0.530248 1011001−0.327094 0.416570 1011010 −0.635577 0.561146 1011011 −0.777941 0.6270401011100 −0.406760 0.706463 1011101 −0.454097 0.890952 1011110 −0.5549360.677703 1011111 −0.616155 0.785695 1100000 −0.215659 −0.071275 1100001−0.247193 −0.239779 1100010 −0.059723 −0.089476 1100011 −0.084352−0.256286 1100100 −0.631601 −0.086959 1100101 −0.421425 −0.0609571100110 −0.811036 −0.081198 1100111 −0.989141 −0.115779 1101000−0.238961 −0.619410 1101001 −0.188755 −0.432433 1101010 −0.081970−0.619772 1101011 −0.071916 −0.446011 1101100 −0.230093 −0.7986931101101 −0.278409 −0.959192 1101110 −0.079376 −0.797516 1101111−0.102980 −0.994337 1110000 −0.540893 −0.373750 1110001 −0.390688−0.300381 1110010 −0.711286 −0.403395 1110011 −0.878402 −0.4771311110100 −0.613230 −0.218230 1110101 −0.459120 −0.180142 1110110−0.770540 −0.249889 1110111 −0.951364 −0.303258 1111000 −0.419831−0.530248 1111001 −0.327094 −0.416570 1111010 −0.635577 −0.5611461111011 −0.777941 −0.627040 1111100 −0.406760 −0.706463 1111101−0.454097 −0.890952 1111110 −0.554936 −0.677703 1111111 −0.616155−0.785695

TABLE 26A SYMBOL COORDINATE BITS X Y 00000000 0.729468 0.681354 000000010.738514 0.673491 00000010 0.855792 0.514140 00000011 0.849844 0.51537900000100 0.968926 0.244322 00000101 0.961654 0.274266 00000110 0.8464390.172785 00000111 0.814534 0.289437 00001000 0.660833 0.597951 000010010.635704 0.601179 00001010 0.703246 0.498537 00001011 0.713555 0.45834200001100 0.982752 0.108821 00001101 0.995743 0.075153 00001110 0.8352160.108792 00001111 0.734334 0.299494 00010000 0.563531 0.824212 000100010.538599 0.841459 00010010 0.422490 0.436968 00010011 0.486743 0.46030300010100 0.533243 0.050591 00010101 0.625049 0.049186 00010110 0.4601590.327276 00010111 0.545204 0.349786 00011000 0.466690 0.722489 000110010.472883 0.710099 00011010 0.416973 0.618858 00011011 0.459806 0.56834700011100 0.496124 0.136766 00011101 0.632908 0.115646 00011110 0.4780720.233508 00011111 0.637346 0.269821 00100000 0.150085 0.986638 001000010.096333 0.982163 00100010 0.054634 0.530674 00100011 0.124963 0.48348800100100 0.039722 0.038334 00100101 0.135172 0.056012 00100110 0.0556950.397262 00100111 0.117755 0.376976 00101000 0.077604 0.807366 001010010.114272 0.876917 00101010 0.077226 0.661268 00101011 0.142363 0.59963500101100 0.048885 0.160450 00101101 0.167945 0.151950 00101110 0.0463400.256559 00101111 0.151392 0.268874 00110000 0.368991 0.926086 001100010.380645 0.924004 00110010 0.333044 0.460912 00110011 0.244729 0.47350500110100 0.373900 0.043782 00110101 0.245282 0.046720 00110110 0.3381220.327772 00110111 0.246479 0.355455 00111000 0.271941 0.776781 001110010.314659 0.780426 00111010 0.281591 0.667979 00111011 0.269267 0.63131300111100 0.391733 0.132460 00111101 0.267292 0.162978 00111110 0.3756660.240801 00111111 0.260740 0.241834 01000000 0.729468 −0.681354 010000010.738514 −0.673491 01000010 0.855792 −0.514140 01000011 0.849844−0.515379 01000100 0.968926 −0.244322 01000101 0.961654 −0.27426601000110 0.846439 −0.172785 01000111 0.814534 −0.289437 010010000.660833 −0.597951 01001001 0.635704 −0.601179 01001010 0.703246−0.498537 01001011 0.713555 −0.458342 01001100 0.982752 −0.10882101001101 0.995743 −0.075153 01001110 0.835216 −0.108792 010011110.734334 −0.299494 01010000 0.563531 −0.824212 01010001 0.538599−0.841459 01010010 0.422490 −0.436968 01010011 0.486743 −0.46030301010100 0.533243 −0.050591 01010101 0.625049 −0.049186 010101100.460159 −0.327276 01010111 0.545204 −0.349786 01011000 0.466690−0.722489 01011001 0.472883 −0.710099 01011010 0.416973 −0.61885801011011 0.459806 −0.568347 01011100 0.496124 −0.136766 010111010.632908 −0.115646 01011110 0.478072 −0.233508 01011111 0.637346−0.269821 01100000 0.150085 −0.986638 01100001 0.096333 −0.98216301100010 0.054634 −0.530674 01100011 0.124963 −0.483488 011001000.039722 −0.038334 01100101 0.135172 −0.056012 01100110 0.055695−0.397262 01100111 0.117755 −0.376976 01101000 0.077604 −0.80736601101001 0.114272 −0.876917 01101010 0.077226 −0.661268 011010110.142363 −0.599635 01101100 0.048885 −0.160450 01101101 0.167945−0.151950 01101110 0.046340 −0.256559 01101111 0.151392 −0.26887401110000 0.368991 −0.926086 01110001 0.380645 −0.924004 011100100.333044 −0.460912 01110011 0.244729 −0.473505 01110100 0.373900−0.043782 01110101 0.245282 −0.046720 01110110 0.338122 −0.32777201110111 0.246479 −0.355455 01111000 0.271941 −0.776781 011110010.314659 −0.780426 01111010 0.281591 −0.667979 01111011 0.269267−0.631313 01111100 0.391733 −0.132460 01111101 0.267292 −0.16297801111110 0.375666 −0.240801 01111111 0.260740 −0.241834 10000000−0.729468 0.681354 10000001 −0.738514 0.673491 10000010 −0.8557920.514140 10000011 −0.849844 0.515379 10000100 −0.968926 0.24432210000101 −0.961654 0.274266 10000110 −0.846439 0.172785 10000111−0.814534 0.289437 10001000 −0.660833 0.597951 10001001 −0.6357040.601179 10001010 −0.703246 0.498537 10001011 −0.713555 0.45834210001100 −0.982752 0.108821 10001101 −0.995743 0.075153 10001110−0.835216 0.108792 10001111 −0.734334 0.299494 10010000 −0.5635310.824212 10010001 −0.538599 0.841459 10010010 −0.422490 0.43696810010011 −0.486743 0.460303 10010100 −0.533243 0.050591 10010101−0.625049 0.049186 10010110 −0.460159 0.327276 10010111 −0.5452040.349786 10011000 −0.466690 0.722489 10011001 −0.472883 0.71009910011010 −0.416973 0.618858 10011011 −0.459806 0.568347 10011100−0.496124 0.136766 10011101 −0.632908 0.115646 10011110 −0.4780720.233508 10011111 −0.637346 0.269821 10100000 −0.150085 0.98663810100001 −0.096333 0.982163 10100010 −0.054634 0.530674 10100011−0.124963 0.483488 10100100 −0.039722 0.038334 10100101 −0.1351720.056012 10100110 −0.055695 0.397262 10100111 −0.117755 0.37697610101000 −0.077604 0.807366 10101001 −0.114272 0.876917 10101010−0.077226 0.661268 10101011 −0.142363 0.599635 10101100 −0.0488850.160450 10101101 −0.167945 0.151950 10101110 −0.046340 0.25655910101111 −0.151392 0.268874 10110000 −0.368991 0.926086 10110001−0.380645 0.924004 10110010 −0.333044 0.460912 10110011 −0.2447290.473505 10110100 −0.373900 0.043782 10110101 −0.245282 0.04672010110110 −0.338122 0.327772 10110111 −0.246479 0.355455 10111000−0.271941 0.776781 10111001 −0.314659 0.780426 10111010 −0.2815910.667979 10111011 −0.269267 0.631313 10111100 −0.391733 0.13246010111101 −0.267292 0.162978 10111110 −0.375666 0.240801 10111111−0.260740 0.241834 11000000 −0.729468 −0.681354 11000001 −0.738514−0.673491 11000010 −0.855792 −0.514140 11000011 −0.849844 −0.51537911000100 −0.968926 −0.244322 11000101 −0.961654 −0.274266 11000110−0.846439 −0.172785 11000111 −0.814534 −0.289437 11001000 −0.660833−0.597951 11001001 −0.635704 −0.601179 11001010 −0.703246 −0.49853711001011 −0.713555 −0.458342 11001100 −0.982752 −0.108821 11001101−0.995743 −0.075153 11001110 −0.835216 −0.108792 11001111 −0.734334−0.299494 11010000 −0.563531 −0.824212 11010001 −0.538599 −0.84145911010010 −0.422490 −0.436968 11010011 −0.486743 −0.460303 11010100−0.533243 −0.050591 11010101 −0.625049 −0.049186 11010110 −0.460159−0.327276 11010111 −0.545204 −0.349786 11011000 −0.466690 −0.72248911011001 −0.472883 −0.710099 11011010 −0.416973 −0.618858 11011011−0.459806 −0.568347 11011100 −0.496124 −0.136766 11011101 −0.632908−0.115646 11011110 −0.478072 −0.233508 11011111 −0.637346 −0.26982111100000 −0.150085 −0.986638 11100001 −0.096333 −0.982163 11100010−0.054634 −0.530674 11100011 −0.124963 −0.483488 11100100 −0.039722−0.038334 11100101 −0.135172 −0.056012 11100110 −0.055695 −0.39726211100111 −0.117755 −0.376976 11101000 −0.077604 −0.807366 11101001−0.114272 −0.876917 11101010 −0.077226 −0.661268 11101011 −0.142363−0.599635 11101100 −0.048885 −0.160450 11101101 −0.167945 −0.15195011101110 −0.046340 −0.256559 11101111 −0.151392 −0.268874 11110000−0.368991 −0.926086 11110001 −0.380645 −0.924004 11110010 −0.333044−0.460912 11110011 −0.244729 −0.473505 11110100 −0.373900 −0.04378211110101 −0.245282 −0.046720 11110110 −0.338122 −0.327772 11110111−0.246479 −0.355455 11111000 −0.271941 −0.776781 11111001 −0.314659−0.780426 11111010 −0.281591 −0.667979 11111011 −0.269267 −0.63131311111100 −0.391733 −0.132460 11111101 −0.267292 −0.162978 11111110−0.375666 −0.240801 11111111 −0.260740 −0.241834

TABLE 26B SYMBOL COORDINATE BITS X Y 00000000 0.100722 0.994770 000000010.750351 0.661022 00000010 0.881575 0.471414 00000011 0.873252 0.48369300000100 0.992123 0.101906 00000101 0.913440 0.102519 00000110 0.9517890.302746 00000111 0.937645 0.339561 00001000 0.672550 0.570706 000010010.676544 0.624432 00001010 0.698643 0.418766 00001011 0.776531 0.39331700001100 0.761618 0.102135 00001101 0.834592 0.108693 00001110 0.7075150.282568 00001111 0.814401 0.272917 00010000 0.492252 0.870452 000100010.594583 0.796236 00010010 0.508862 0.423943 00010011 0.436952 0.51204300010100 0.427335 0.024507 00010101 0.472640 0.103214 00010110 0.5045870.325416 00010111 0.481372 0.201663 00011000 0.497458 0.750636 000110010.516303 0.690518 00011010 0.579766 0.455486 00011011 0.502377 0.57074900011100 0.663972 0.082265 00011101 0.584150 0.076688 00011110 0.6109690.277009 00011111 0.572290 0.199840 00100000 0.056666 0.691228 001000010.151272 0.675756 00100010 0.204894 0.530525 00100011 0.216699 0.58437900100100 0.043480 0.044961 00100101 0.049099 0.162247 00100110 0.0382370.360110 00100111 0.049416 0.284838 00101000 0.099703 0.839454 001010010.117273 0.821271 00101010 0.135244 0.463140 00101011 0.031880 0.52995300101100 0.162184 0.047275 00101101 0.125789 0.162121 00101110 0.1176110.404115 00101111 0.138289 0.256313 00110000 0.343736 0.937804 001100010.259185 0.697227 00110010 0.338770 0.448588 00110011 0.336399 0.57873600110100 0.326500 0.064530 00110101 0.345811 0.144428 00110110 0.3809060.330718 00110111 0.374826 0.247547 00111000 0.314588 0.835245 001110010.330246 0.739962 00111010 0.261873 0.406571 00111011 0.397693 0.62272300111100 0.242090 0.072399 00111101 0.232395 0.167109 00111110 0.2381750.347737 00111111 0.249935 0.249763 01000000 0.100722 −0.994770 010000010.750351 −0.661022 01000010 0.881575 −0.471414 01000011 0.873252−0.483693 01000100 0.992123 −0.101906 01000101 0.913440 −0.10251901000110 0.951789 −0.302746 01000111 0.937645 −0.339561 010010000.672550 −0.570706 01001001 0.676544 −0.624432 01001010 0.698643−0.418766 01001011 0.776531 −0.393317 01001100 0.761618 −0.10213501001101 0.834592 −0.108693 01001110 0.707515 −0.282568 010011110.814401 −0.272917 01010000 0.492252 −0.870452 01010001 0.594583−0.796236 01010010 0.508862 −0.423943 01010011 0.436952 −0.51204301010100 0.427335 −0.024507 01010101 0.472640 −0.103214 010101100.504587 −0.325416 01010111 0.481372 −0.201663 01011000 0.497458−0.750636 01011001 0.516303 −0.690518 01011010 0.579766 −0.45548601011011 0.502377 −0.570749 01011100 0.663972 −0.082265 010111010.584150 −0.076688 01011110 0.610969 −0.277009 01011111 0.572290−0.199840 01100000 0.056666 −0.691228 01100001 0.151272 −0.67575601100010 0.204894 −0.530525 01100011 0.216699 −0.584379 011001000.043480 −0.044961 01100101 0.049099 −0.162247 01100110 0.038237−0.360110 01100111 0.049416 −0.284838 01101000 0.099703 −0.83945401101001 0.117273 −0.821271 01101010 0.135244 −0.463140 011010110.031880 −0.529953 01101100 0.162184 −0.047275 01101101 0.125789−0.162121 01101110 0.117611 −0.404115 01101111 0.138289 −0.25631301110000 0.343736 −0.937804 01110001 0.259185 −0.697227 011100100.338770 −0.448588 01110011 0.336399 −0.578736 01110100 0.326500−0.064530 01110101 0.345811 −0.144428 01110110 0.380906 −0.33071801110111 0.374826 −0.247547 01111000 0.314588 −0.835245 011110010.330246 −0.739962 01111010 0.261873 −0.406571 01111011 0.397693−0.622723 01111100 0.242090 −0.072399 01111101 0.232395 −0.16710901111110 0.238175 −0.347737 01111111 0.249935 −0.249763 10000000−0.100722 0.994770 10000001 −0.750351 0.661022 10000010 −0.8815750.471414 10000011 −0.873252 0.483693 10000100 −0.992123 0.10190610000101 −0.913440 0.102519 10000110 −0.951789 0.302746 10000111−0.937645 0.339561 10001000 −0.672550 0.570706 10001001 −0.6765440.624432 10001010 −0.698643 0.418766 10001011 −0.776531 0.39331710001100 −0.761618 0.102135 10001101 −0.834592 0.108693 10001110−0.707515 0.282568 10001111 −0.814401 0.272917 10010000 −0.4922520.870452 10010001 −0.594583 0.796236 10010010 −0.508862 0.42394310010011 −0.436952 0.512043 10010100 −0.427335 0.024507 10010101−0.472640 0.103214 10010110 −0.504587 0.325416 10010111 −0.4813720.201663 10011000 −0.497458 0.750636 10011001 −0.516303 0.69051810011010 −0.579766 0.455486 10011011 −0.502377 0.570749 10011100−0.663972 0.082265 10011101 −0.584150 0.076688 10011110 −0.6109690.277009 10011111 −0.572290 0.199840 10100000 −0.056666 0.69122810100001 −0.151272 0.675756 10100010 −0.204894 0.530525 10100011−0.216699 0.584379 10100100 −0.043480 0.044961 10100101 −0.0490990.162247 10100110 −0.038237 0.360110 10100111 −0.049416 0.28483810101000 −0.099703 0.839454 10101001 −0.117273 0.821271 10101010−0.135244 0.463140 10101011 −0.031880 0.529953 10101100 −0.1621840.047275 10101101 −0.125789 0.162121 10101110 −0.117611 0.40411510101111 −0.138289 0.256313 10110000 −0.343736 0.937804 10110001−0.259185 0.697227 10110010 −0.338770 0.448588 10110011 −0.3363990.578736 10110100 −0.326500 0.064530 10110101 −0.345811 0.14442810110110 −0.380906 0.330718 10110111 −0.374826 0.247547 10111000−0.314588 0.835245 10111001 −0.330246 0.739962 10111010 −0.2618730.406571 10111011 −0.397693 0.622723 10111100 −0.242090 0.07239910111101 −0.232395 0.167109 10111110 −0.238175 0.347737 10111111−0.249935 0.249763 11000000 −0.100722 −0.994770 11000001 −0.750351−0.661022 11000010 −0.881575 −0.471414 11000011 −0.873252 −0.48369311000100 −0.992123 −0.101906 11000101 −0.913440 −0.102519 11000110−0.951789 −0.302746 11000111 −0.937645 −0.339561 11001000 −0.672550−0.570706 11001001 −0.676544 −0.624432 11001010 −0.698643 −0.41876611001011 −0.776531 −0.393317 11001100 −0.761618 −0.102135 11001101−0.834592 −0.108693 11001110 −0.707515 −0.282568 11001111 −0.814401−0.272917 11010000 −0.492252 −0.870452 11010001 −0.594583 −0.79623611010010 −0.508862 −0.423943 11010011 −0.436952 −0.512043 11010100−0.427335 −0.024507 11010101 −0.472640 −0.103214 11010110 −0.504587−0.325416 11010111 −0.481372 −0.201663 11011000 −0.497458 −0.75063611011001 −0.516303 −0.690518 11011010 −0.579766 −0.455486 11011011−0.502377 −0.570749 11011100 −0.663972 −0.082265 11011101 −0.584150−0.076688 11011110 −0.610969 −0.277009 11011111 −0.572290 −0.19984011100000 −0.056666 −0.691228 11100001 −0.151272 −0.675756 11100010−0.204894 −0.530525 11100011 −0.216699 −0.584379 11100100 −0.043480−0.044961 11100101 −0.049099 −0.162247 11100110 −0.038237 −0.36011011100111 −0.049416 −0.284838 11101000 −0.099703 −0.839454 11101001−0.117273 −0.821271 11101010 −0.135244 −0.463140 11101011 −0.031880−0.529953 11101100 −0.162184 −0.047275 11101101 −0.125789 −0.16212111101110 −0.117611 −0.404115 11101111 −0.138289 −0.256313 11110000−0.343736 −0.937804 11110001 −0.259185 −0.697227 11110010 −0.338770−0.448588 11110011 −0.336399 −0.578736 11110100 −0.326500 −0.06453011110101 −0.345811 −0.144428 11110110 −0.380906 −0.330718 11110111−0.374826 −0.247547 11111000 −0.314588 −0.835245 11111001 −0.330246−0.739962 11111010 −0.261873 −0.406571 11111011 −0.397693 −0.62272311111100 −0.242090 −0.072399 11111101 −0.232395 −0.167109 11111110−0.238175 −0.347737 11111111 −0.249935 −0.249763

TABLE 26C SYMBOL COORDINATE BITS X Y 00000000 0.704805 0.709401 000000010.653485 0.647271 00000010 0.839635 0.536645 00000011 0.779762 0.46641800000100 0.950855 0.309585 00000101 0.898873 0.237975 00000110 0.7915940.179828 00000111 0.816680 0.306330 00001000 0.505509 0.556460 000010010.578086 0.594539 00001010 0.604085 0.430430 00001011 0.675607 0.46747400001100 0.995507 0.093945 00001101 0.927144 0.066550 00001110 0.7984160.068850 00001111 0.692878 0.075290 00010000 0.479391 0.863511 000100010.505225 0.774265 00010010 0.484617 0.414350 00010011 0.520888 0.31095700010100 0.381499 0.038864 00010101 0.487670 0.092097 00010110 0.4118490.258755 00010111 0.487732 0.202001 00011000 0.406573 0.655126 000110010.462736 0.718925 00011010 0.664047 0.289395 00011011 0.596484 0.26420300011100 0.355974 0.107909 00011101 0.560999 0.039644 00011110 0.3595730.187393 00011111 0.615102 0.131990 00100000 0.115389 0.992829 001000010.099077 0.892498 00100010 0.049649 0.509714 00100011 0.145149 0.48357700100100 0.041063 0.109972 00100101 0.054519 0.039305 00100110 0.0566360.417591 00100111 0.146141 0.395735 00101000 0.120064 0.703253 001010010.072859 0.801344 00101010 0.058365 0.627881 00101011 0.138895 0.59027600101100 0.039437 0.207733 00101101 0.107948 0.211695 00101110 0.0441170.330946 00101111 0.135942 0.306297 00110000 0.296688 0.951488 001100010.300001 0.845945 00110010 0.381891 0.443738 00110011 0.259783 0.46515200110100 0.258503 0.034355 00110101 0.161844 0.058432 00110110 0.3661990.349348 00110111 0.261819 0.363870 00111000 0.262841 0.689677 001110010.249677 0.780505 00111010 0.347351 0.553715 00111011 0.238875 0.56914600111100 0.254190 0.129082 00111101 0.178447 0.154862 00111110 0.2854100.232281 00111111 0.211277 0.280009 01000000 0.704805 −0.709401 010000010.653485 −0.647271 01000010 0.839635 −0.536645 01000011 0.779762−0.466418 01000100 0.950855 −0.309585 01000101 0.898873 −0.23797501000110 0.791594 −0.179828 01000111 0.816680 −0.306330 010010000.505509 −0.556460 01001001 0.578086 −0.594539 01001010 0.604085−0.430430 01001011 0.675607 −0.467474 01001100 0.995507 −0.09394501001101 0.927144 −0.066550 01001110 0.798416 −0.068850 010011110.692878 −0.075290 01010000 0.479391 −0.863511 01010001 0.505225−0.774265 01010010 0.484617 −0.414350 01010011 0.520888 −0.31095701010100 0.381499 −0.038864 01010101 0.487670 −0.092097 010101100.411849 −0.258755 01010111 0.487732 −0.202001 01011000 0.406573−0.655126 01011001 0.462736 −0.718925 01011010 0.664047 −0.28939501011011 0.596484 −0.264203 01011100 0.355974 −0.107909 010111010.560999 −0.039644 01011110 0.359573 −0.187393 01011111 0.615102−0.131990 01100000 0.115389 −0.992829 01100001 0.099077 −0.89249801100010 0.049649 −0.509714 01100011 0.145149 −0.483577 011001000.041063 −0.109972 01100101 0.054519 −0.039305 01100110 0.056636−0.417591 01100111 0.146141 −0.395735 01101000 0.120064 −0.70325301101001 0.072859 −0.801344 01101010 0.058365 −0.627881 011010110.138895 −0.590276 01101100 0.039437 −0.207733 01101101 0.107948−0.211695 01101110 0.044117 −0.330946 01101111 0.135942 −0.30629701110000 0.296688 −0.951488 01110001 0.300001 −0.845945 011100100.381891 −0.443738 01110011 0.259783 −0.465152 01110100 0.258503−0.034355 01110101 0.161844 −0.058432 01110110 0.366199 −0.34934801110111 0.261819 −0.363870 01111000 0.262841 −0.689677 011110010.249677 −0.780505 01111010 0.347351 −0.553715 01111011 0.238875−0.569146 01111100 0.254190 −0.129082 01111101 0.178447 −0.15486201111110 0.285410 −0.232281 01111111 0.211277 −0.280009 10000000−0.704805 0.709401 10000001 −0.653485 0.647271 10000010 −0.8396350.536645 10000011 −0.779762 0.466418 10000100 −0.950855 0.30958510000101 −0.898873 0.237975 10000110 −0.791594 0.179828 10000111−0.816680 0.306330 10001000 −0.505509 0.556460 10001001 −0.5780860.594539 10001010 −0.604085 0.430430 10001011 −0.675607 0.46747410001100 −0.995507 0.093945 10001101 −0.927144 0.066550 10001110−0.798416 0.068850 10001111 −0.692878 0.075290 10010000 −0.4793910.863511 10010001 −0.505225 0.774265 10010010 −0.484617 0.41435010010011 −0.520888 0.310957 10010100 −0.381499 0.038864 10010101−0.487670 0.092097 10010110 −0.411849 0.258755 10010111 −0.4877320.202001 10011000 −0.406573 0.655126 10011001 −0.462736 0.71892510011010 −0.664047 0.289395 10011011 −0.596484 0.264203 10011100−0.355974 0.107909 10011101 −0.560999 0.039644 10011110 −0.3595730.187393 10011111 −0.615102 0.131990 10100000 −0.115389 0.99282910100001 −0.099077 0.892498 10100010 −0.049649 0.509714 10100011−0.145149 0.483577 10100100 −0.041063 0.109972 10100101 −0.0545190.039305 10100110 −0.056636 0.417591 10100111 −0.146141 0.39573510101000 −0.120064 0.703253 10101001 −0.072859 0.801344 10101010−0.058365 0.627881 10101011 −0.138895 0.590276 10101100 −0.0394370.207733 10101101 −0.107948 0.211695 10101110 −0.044117 0.33094610101111 −0.135942 0.306297 10110000 −0.296688 0.951488 10110001−0.300001 0.845945 10110010 −0.381891 0.443738 10110011 −0.2597830.465152 10110100 −0.258503 0.034355 10110101 −0.161844 0.05843210110110 −0.366199 0.349348 10110111 −0.261819 0.363870 10111000−0.262841 0.689677 10111001 −0.249677 0.780505 10111010 −0.3473510.553715 10111011 −0.238875 0.569146 10111100 −0.254190 0.12908210111101 −0.178447 0.154862 10111110 −0.285410 0.232281 10111111−0.211277 0.280009 11000000 −0.704805 −0.709401 11000001 −0.653485−0.647271 11000010 −0.839635 −0.536645 11000011 −0.779762 −0.46641811000100 −0.950855 −0.309585 11000101 −0.898873 −0.237975 11000110−0.791594 −0.179828 11000111 −0.816680 −0.306330 11001000 −0.505509−0.556460 11001001 −0.578086 −0.594539 11001010 −0.604085 −0.43043011001011 −0.675607 −0.467474 11001100 −0.995507 −0.093945 11001101−0.927144 −0.066550 11001110 −0.798416 −0.068850 11001111 −0.692878−0.075290 11010000 −0.479391 −0.863511 11010001 −0.505225 −0.77426511010010 −0.484617 −0.414350 11010011 −0.520888 −0.310957 11010100−0.381499 −0.038864 11010101 −0.487670 −0.092097 11010110 −0.411849−0.258755 11010111 −0.487732 −0.202001 11011000 −0.406573 −0.65512611011001 −0.462736 −0.718925 11011010 −0.664047 −0.289395 11011011−0.596484 −0.264203 11011100 −0.355974 −0.107909 11011101 −0.560999−0.039644 11011110 −0.359573 −0.187393 11011111 −0.615102 −0.13199011100000 −0.115389 −0.992829 11100001 −0.099077 −0.892498 11100010−0.049649 −0.509714 11100011 −0.145149 −0.483577 11100100 −0.041063−0.109972 11100101 −0.054519 −0.039305 11100110 −0.056636 −0.41759111100111 −0.146141 −0.395735 11101000 −0.120064 −0.703253 11101001−0.072859 −0.801344 11101010 −0.058365 −0.627881 11101011 −0.138895−0.590276 11101100 −0.039437 −0.207733 11101101 −0.107948 −0.21169511101110 −0.044117 −0.330946 11101111 −0.135942 −0.306297 11110000−0.296688 −0.951488 11110001 −0.300001 −0.845945 11110010 −0.381891−0.443738 11110011 −0.259783 −0.465152 11110100 −0.258503 −0.03435511110101 −0.161844 −0.058432 11110110 −0.366199 −0.349348 11110111−0.261819 −0.363870 11111000 −0.262841 −0.689677 11111001 −0.249677−0.780505 11111010 −0.347351 −0.553715 11111011 −0.238875 −0.56914611111100 −0.254190 −0.129082 11111101 −0.178447 −0.154862 11111110−0.285410 −0.232281 11111111 −0.211277 −0.280009

Through the descriptions of the preceding embodiments, the presentinvention may be implemented by using hardware only or by using softwareand a necessary universal hardware platform. Based on suchunderstandings, the technical solution of the present invention may beembodied in the form of a software product. The software product may bestored in a non-volatile or non-transitory storage medium, which can bea compact disk read-only memory (CD-ROM), USB flash disk, or a removablehard disk. The software product includes a number of instructions thatenable a computer device (personal computer, server, or network device)to execute the methods provided in the embodiments of the presentinvention. For example, such an execution may correspond to a simulationof the logical operations as described herein. The software product mayadditionally or alternatively include number of instructions that enablea computer device to execute operations for configuring or programming adigital logic apparatus in accordance with embodiments of the presentinvention.

Although the present invention has been described with reference tospecific features and embodiments thereof, it is evident that variousmodifications and combinations can be made thereto without departingfrom the invention. The specification and drawings are, accordingly, tobe regarded simply as an illustration of the invention as defined by theappended claims, and are contemplated to cover any and allmodifications, variations, combinations or equivalents that fall withinthe scope of the present invention.

What is claimed is:
 1. A method for wireless communication using digitalquadrature amplitude modulation (QAM), the method comprising:translating between constellation symbols and bit sequencescorresponding to the constellation symbols using a mapping moduleelectronic component of a wireless communication device, in accordancewith a 256-point constellation; wherein normalized magnitudes of theconstellation symbols in a first quadrant of the 256-point constellationare defined by the following coordinate pairs to at least three decimalplaces of precision: 0.975369 1.374032 1.481139 0.719889 1.2180200.537432 1.572273 1.013574 1.187472 0.140021 1.528894 0.437163 1.2094280.325388 1.451803 0.133447 1.150324 0.991883 0.920560 1.027887 1.1308590.690274 0.935148 0.791094 1.046905 0.109020 0.905564 0.126090 0.9868450.392801 0.888567 0.278893 0.311973 1.734362 0.529664 1.037246 0.6230190.619800 0.545408 0.794517 0.590997 0.100302 0.593410 0.246925 0.6071520.477790 0.629036 0.343531 0.563423 1.365187 0.710907 1.103897 0.7639530.637666 0.728679 0.837901 0.699119 0.052387 0.778520 0.167574 0.8411390.487476 0.768298 0.365852 0.127333 1.155716 0.307801 1.071269 0.0542260.569000 0.045338 0.681811 0.028860 0.067281 0.073608 0.181658 0.0368200.425876 0.052368 0.277893 0.043419 0.999378 0.134293 0.871130 0.1677410.582866 0.144323 0.745869 0.216884 0.055250 0.186854 0.164842 0.1606980.411437 0.184735 0.310456 0.173083 1.310422 0.373110 0.990945 0.4420360.572513 0.450171 0.761992 0.448273 0.078434 0.429733 0.223957 0.4335250.483009 0.442487 0.351997 0.234057 1.493126 0.245349 0.871117 0.2780320.601780 0.299117 0.752566 0.343828 0.049983 0.307660 0.197631 0.2568880.459299 0.301477 0.340566 0.975369 −1.374032 1.481139 −0.7198891.218020 −0.537432 1.572273 −1.013574 1.187472 −0.140021 1.528894−0.437163 1.209428 −0.325388 1.451803 −0.133447 1.150324 −0.9918830.920560 −1.027887 1.130859 −0.690274 0.935148 −0.791094 1.046905−0.109020 0.905564 −0.126090 0.986845 −0.392801 0.888567 −0.2788930.311973 −1.734362 0.529664 −1.037246 0.623019 −0.619800 0.545408−0.794517 0.590997 −0.100302 0.593410 −0.246925 0.607152 −0.4777900.629036 −0.343531 0.563423 −1.365187 0.710907 −1.103897 0.763953−0.637666 0.728679 −0.837901 0.699119 −0.052387 0.778520 −0.1675740.841139 −0.487476 0.768298 −0.365852 0.127333 −1.155716 0.307801−1.071269 0.054226 −0.569000 0.045338 −0.681811 0.028860 −0.0672810.073608 −0.181658 0.036820 −0.425876 0.052368 −0.277893 0.043419−0.999378 0.134293 −0.871130 0.167741 −0.582866 0.144323 −0.7458690.216884 −0.055250 0.186854 −0.164842 0.160698 −0.411437 0.184735−0.310456 0.173083 −1.310422 0.373110 −0.990945 0.442036 −0.5725130.450171 −0.761992 0.448273 −0.078434 0.429733 −0.223957 0.433525−0.483009 0.442487 −0.351997 0.234057 −1.493126 0.245349 −0.8711170.278032 −0.601780 0.299117 −0.752566 0.343828 −0.049983 0.307660−0.197631 0.256888 −0.459299 0.301477 −0.340566 −0.975369 1.374032−1.481139 0.719889 −1.218020 0.537432 −1.572273 1.013574 −1.1874720.140021 −1.528894 0.437163 −1.209428 0.325388 −1.451803 0.133447−1.150324 0.991883 −0.920560 1.027887 −1.130859 0.690274 −0.9351480.791094 −1.046905 0.109020 −0.905564 0.126090 −0.986845 0.392801−0.888567 0.278893 −0.311973 1.734362 −0.529664 1.037246 −0.6230190.619800 −0.545408 0.794517 −0.590997 0.100302 −0.593410 0.246925−0.607152 0.477790 −0.629036 0.343531 −0.563423 1.365187 −0.7109071.103897 −0.763953 0.637666 −0.728679 0.837901 −0.699119 0.052387−0.778520 0.167574 −0.841139 0.487476 −0.768298 0.365852 −0.1273331.155716 −0.307801 1.071269 −0.054226 0.569000 −0.045338 0.681811−0.028860 0.067281 −0.073608 0.181658 −0.036820 0.425876 −0.0523680.277893 −0.043419 0.999378 −0.134293 0.871130 −0.167741 0.582866−0.144323 0.745869 −0.216884 0.055250 −0.186854 0.164842 −0.1606980.411437 −0.184735 0.310456 −0.173083 1.310422 −0.373110 0.990945−0.442036 0.572513 −0.450171 0.761992 −0.448273 0.078434 −0.4297330.223957 −0.433525 0.483009 −0.442487 0.351997 −0.234057 1.493126−0.245349 0.871117 −0.278032 0.601780 −0.299117 0.752566 −0.3438280.049983 −0.307660 0.197631 −0.256888 0.459299 −0.301477 0.340566−0.975369 −1.374032 −1.481139 −0.719889 −1.218020 −0.537432 −1.572273−1.013574 −1.187472 −0.140021 −1.528894 −0.437163 −1.209428 −0.325388−1.451803 −0.133447 −1.150324 −0.991883 −0.920560 −1.027887 −1.130859−0.690274 −0.935148 −0.791094 −1.046905 −0.109020 −0.905564 −0.126090−0.986845 −0.392801 −0.888567 −0.278893 −0.311973 −1.734362 −0.529664−1.037246 −0.623019 −0.619800 −0.545408 −0.794517 −0.590997 −0.100302−0.593410 −0.246925 −0.607152 −0.477790 −0.629036 −0.343531 −0.563423−1.365187 −0.710907 −1.103897 −0.763953 −0.637666 −0.728679 −0.837901−0.699119 −0.052387 −0.778520 −0.167574 −0.841139 −0.487476 −0.768298−0.365852 −0.127333 −1.155716 −0.307801 −1.071269 −0.054226 −0.569000−0.045338 −0.681811 −0.028860 −0.067281 −0.073608 −0.181658 −0.036820−0.425876 −0.052368 −0.277893 −0.043419 −0.999378 −0.134293 −0.871130−0.167741 −0.582866 −0.144323 −0.745869 −0.216884 −0.055250 −0.186854−0.164842 −0.160698 −0.411437 −0.184735 −0.310456 −0.173083 −1.310422−0.373110 −0.990945 −0.442036 −0.572513 −0.450171 −0.761992 −0.448273−0.078434 −0.429733 −0.223957 −0.433525 −0.483009 −0.442487 −0.351997−0.234057 −1.493126 −0.245349 −0.871117 −0.278032 −0.601780 −0.299117−0.752566 −0.343828 −0.049983 −0.307660 −0.197631 −0.256888 −0.459299−0.301477 −0.340566;

and transmitting, by a transmitter of the wireless communication device,a wireless signal modulated in accordance with the constellationsymbols.
 2. The method of claim 1, wherein normalized magnitudes of theconstellation symbols in the first quadrant of the 256-pointconstellation are defined by the coordinate pairs to at least fourdecimal places of precision.
 3. The method of claim 1, whereinnormalized magnitudes of the constellation symbols in the first quadrantof the 256-point constellation are defined by the coordinate pairs to atleast five decimal places of precision.
 4. The method of claim 1,wherein normalized magnitudes of the constellation symbols in the firstquadrant of the 256-point constellation are defined by the coordinatepairs to six decimal places of precision.
 5. The method of claim 1,wherein the constellation is a reflection-symmetric constellation. 6.The method of claim 1, wherein: left-hand-side coordinates of thecoordinate pairs represent normalized magnitudes of one of in-phasecomponents of the constellation symbols or quadrature components of theconstellation symbols; and right-hand-side coordinates of the coordinatepairs represent normalized magnitudes of the other one of the in-phasecomponents of the constellation symbols or the quadrature components ofthe constellation symbols.
 7. The method of claim 1, wherein the bitsequences are assigned to the constellation symbols using Gray mapping.8. An apparatus for a wireless communication device configured forwireless communication using digital quadrature amplitude modulation(QAM), the apparatus comprising: a mapping module electronic componentconfigured to translate between constellation symbols and bit sequencescorresponding to the constellation symbols in accordance with a256-point constellation; wherein normalized magnitudes of theconstellation symbols in a first quadrant of the 256-point constellationare defined by the following coordinate pairs to at least three decimalplaces of precision: 0.975369 1.374032 1.481139 0.719889 1.2180200.537432 1.572273 1.013574 1.187472 0.140021 1.528894 0.437163 1.2094280.325388 1.451803 0.133447 1.150324 0.991883 0.920560 1.027887 1.1308590.690274 0.935148 0.791094 1.046905 0.109020 0.905564 0.126090 0.9868450.392801 0.888567 0.278893 0.311973 1.734362 0.529664 1.037246 0.6230190.619800 0.545408 0.794517 0.590997 0.100302 0.593410 0.246925 0.6071520.477790 0.629036 0.343531 0.563423 1.365187 0.710907 1.103897 0.7639530.637666 0.728679 0.837901 0.699119 0.052387 0.778520 0.167574 0.8411390.487476 0.768298 0.365852 0.127333 1.155716 0.307801 1.071269 0.0542260.569000 0.045338 0.681811 0.028860 0.067281 0.073608 0.181658 0.0368200.425876 0.052368 0.277893 0.043419 0.999378 0.134293 0.871130 0.1677410.582866 0.144323 0.745869 0.216884 0.055250 0.186854 0.164842 0.1606980.411437 0.184735 0.310456 0.173083 1.310422 0.373110 0.990945 0.4420360.572513 0.450171 0.761992 0.448273 0.078434 0.429733 0.223957 0.4335250.483009 0.442487 0.351997 0.234057 1.493126 0.245349 0.871117 0.2780320.601780 0.299117 0.752566 0.343828 0.049983 0.307660 0.197631 0.2568880.459299 0.301477 0.340566 0.975369 −1.374032 1.481139 −0.7198891.218020 −0.537432 1.572273 −1.013574 1.187472 −0.140021 1.528894−0.437163 1.209428 −0.325388 1.451803 −0.133447 1.150324 −0.9918830.920560 −1.027887 1.130859 −0.690274 0.935148 −0.791094 1.046905−0.109020 0.905564 −0.126090 0.986845 −0.392801 0.888567 −0.2788930.311973 −1.734362 0.529664 −1.037246 0.623019 −0.619800 0.545408−0.794517 0.590997 −0.100302 0.593410 −0.246925 0.607152 −0.4777900.629036 −0.343531 0.563423 −1.365187 0.710907 −1.103897 0.763953−0.637666 0.728679 −0.837901 0.699119 −0.052387 0.778520 −0.1675740.841139 −0.487476 0.768298 −0.365852 0.127333 −1.155716 0.307801−1.071269 0.054226 −0.569000 0.045338 −0.681811 0.028860 −0.0672810.073608 −0.181658 0.036820 −0.425876 0.052368 −0.277893 0.043419−0.999378 0.134293 −0.871130 0.167741 −0.582866 0.144323 −0.7458690.216884 −0.055250 0.186854 −0.164842 0.160698 −0.411437 0.184735−0.310456 0.173083 −1.310422 0.373110 −0.990945 0.442036 −0.5725130.450171 −0.761992 0.448273 −0.078434 0.429733 −0.223957 0.433525−0.483009 0.442487 −0.351997 0.234057 −1.493126 0.245349 −0.8711170.278032 −0.601780 0.299117 −0.752566 0.343828 −0.049983 0.307660−0.197631 0.256888 −0.459299 0.301477 −0.340566 −0.975369 1.374032−1.481139 0.719889 −1.218020 0.537432 −1.572273 1.013574 −1.1874720.140021 −1.528894 0.437163 −1.209428 0.325388 −1.451803 0.133447−1.150324 0.991883 −0.920560 1.027887 −1.130859 0.690274 −0.9351480.791094 −1.046905 0.109020 −0.905564 0.126090 −0.986845 0.392801−0.888567 0.278893 −0.311973 1.734362 −0.529664 1.037246 −0.6230190.619800 −0.545408 0.794517 −0.590997 0.100302 −0.593410 0.246925−0.607152 0.477790 −0.629036 0.343531 −0.563423 1.365187 −0.7109071.103897 −0.763953 0.637666 −0.728679 0.837901 −0.699119 0.052387−0.778520 0.167574 −0.841139 0.487476 −0.768298 0.365852 −0.1273331.155716 −0.307801 1.071269 −0.054226 0.569000 −0.045338 0.681811−0.028860 0.067281 −0.073608 0.181658 −0.036820 0.425876 −0.0523680.277893 −0.043419 0.999378 −0.134293 0.871130 −0.167741 0.582866−0.144323 0.745869 −0.216884 0.055250 −0.186854 0.164842 −0.1606980.411437 −0.184735 0.310456 −0.173083 1.310422 −0.373110 0.990945−0.442036 0.572513 −0.450171 0.761992 −0.448273 0.078434 −0.4297330.223957 −0.433525 0.483009 −0.442487 0.351997 −0.234057 1.493126−0.245349 0.871117 −0.278032 0.601780 −0.299117 0.752566 −0.3438280.049983 −0.307660 0.197631 −0.256888 0.459299 −0.301477 0.340566−0.975369 −1.374032 −1.481139 −0.719889 −1.218020 −0.537432 −1.572273−1.013574 −1.187472 −0.140021 −1.528894 −0.437163 −1.209428 −0.325388−1.451803 −0.133447 −1.150324 −0.991883 −0.920560 −1.027887 −1.130859−0.690274 −0.935148 −0.791094 −1.046905 −0.109020 −0.905564 −0.126090−0.986845 −0.392801 −0.888567 −0.278893 −0.311973 −1.734362 −0.529664−1.037246 −0.623019 −0.619800 −0.545408 −0.794517 −0.590997 −0.100302−0.593410 −0.246925 −0.607152 −0.477790 −0.629036 −0.343531 −0.563423−1.365187 −0.710907 −1.103897 −0.763953 −0.637666 −0.728679 −0.837901−0.699119 −0.052387 −0.778520 −0.167574 −0.841139 −0.487476 −0.768298−0.365852 −0.127333 −1.155716 −0.307801 −1.071269 −0.054226 −0.569000−0.045338 −0.681811 −0.028860 −0.067281 −0.073608 −0.181658 −0.036820−0.425876 −0.052368 −0.277893 −0.043419 −0.999378 −0.134293 −0.871130−0.167741 −0.582866 −0.144323 −0.745869 −0.216884 −0.055250 −0.186854−0.164842 −0.160698 −0.411437 −0.184735 −0.310456 −0.173083 −1.310422−0.373110 −0.990945 −0.442036 −0.572513 −0.450171 −0.761992 −0.448273−0.078434 −0.429733 −0.223957 −0.433525 −0.483009 −0.442487 −0.351997−0.234057 −1.493126 −0.245349 −0.871117 −0.278032 −0.601780 −0.299117−0.752566 −0.343828 −0.049983 −0.307660 −0.197631 −0.256888 −0.459299−0.301477 −0.340566;

and a transmitter configured to transmit a wireless signal modulated inaccordance with the constellation symbols.
 9. The apparatus of claim 8,wherein normalized magnitudes of the constellation symbols in the firstquadrant of the 256-point constellation are defined by the coordinatepairs to at least four decimal places of precision.
 10. The apparatus ofclaim 8, wherein normalized magnitudes of the constellation symbols inthe first quadrant of the 256-point constellation are defined by thecoordinate pairs to at least five decimal places of precision.
 11. Theapparatus of claim 8, wherein normalized magnitudes of the constellationsymbols in the first quadrant of the 256-point constellation are definedby the coordinate pairs to six decimal places of precision.
 12. Theapparatus of claim 8, wherein the constellation is areflection-symmetric constellation.
 13. The apparatus of claim 8,wherein: left-hand-side coordinates the coordinate pairs representnormalized magnitudes of one of in-phase components of the constellationsymbols or quadrature components of the constellation symbols; andright-hand-side coordinates of the coordinate pairs represent normalizedmagnitudes of the other one of the in-phase components of theconstellation symbols or the quadrature components of the constellationsymbols.
 14. The apparatus of claim 8, wherein the bit sequences areassigned to the constellation symbols using Gray mapping.
 15. A methodfor wireless communication using digital quadrature amplitude modulation(QAM), the method comprising: translating between constellation symbolsand bit sequences corresponding to the constellation symbols using amapping module electronic component of a wireless communication device,in accordance with a 128-point constellation; wherein normalizedmagnitudes of the constellation symbols in a first quadrant of the128-point constellation are defined by the following coordinate pairs toat least three decimal places of precision: 0.752060 0.302196 0.7889830.113122 0.325356 0.054462 0.573961 0.098934 0.579122 0.497202 0.4717760.396048 0.294917 0.133438 0.433938 0.245088 0.132847 0.742015 0.1222530.604949 0.068657 0.075472 0.060983 0.445207 0.382346 0.652673 0.3020640.494450 0.166497 0.233502 0.196116 0.340897 0.907567 0.452354 1.0439220.158157 1.130081 0.548716 1.320594 0.181413 0.712483 0.646623 0.8155260.865815 1.157076 0.928991 1.532471 0.508968 0.120519 0.915797 0.1482591.123784 0.282652 1.690100 0.221465 1.387236 0.423824 0.821654 0.4887041.037583 0.872546 1.413810 0.675009 1.247576 0.752060 −0.302196 0.788983−0.113122 0.325356 −0.054462 0.573961 −0.098934 0.579122 −0.4972020.471776 −0.396048 0.294917 −0.133438 0.433938 −0.245088 0.132847−0.742015 0.122253 −0.604949 0.068657 −0.075472 0.060983 −0.4452070.382346 −0.652673 0.302064 −0.494450 0.166497 −0.233502 0.196116−0.340897 0.907567 −0.452354 1.043922 −0.158157 1.130081 −0.5487161.320594 −0.181413 0.712483 −0.646623 0.815526 −0.865815 1.157076−0.928991 1.532471 −0.508968 0.120519 −0.915797 0.148259 −1.1237840.282652 −1.690100 0.221465 −1.387236 0.423824 −0.821654 0.488704−1.037583 0.872546 −1.413810 0.675009 −1.247576 −0.752060 0.302196−0.788983 0.113122 −0.325356 0.054462 −0.573961 0.098934 −0.5791220.497202 −0.471776 0.396048 −0.294917 0.133438 −0.433938 0.245088−0.132847 0.742015 −0.122253 0.604949 −0.068657 0.075472 −0.0609830.445207 −0.382346 0.652673 −0.302064 0.494450 −0.166497 0.233502−0.196116 0.340897 −0.907567 0.452354 −1.043922 0.158157 −1.1300810.548716 −1.320594 0.181413 −0.712483 0.646623 −0.815526 0.865815−1.157076 0.928991 −1.532471 0.508968 −0.120519 0.915797 −0.1482591.123784 −0.282652 1.690100 −0.221465 1.387236 −0.423824 0.821654−0.488704 1.037583 −0.872546 1.413810 −0.675009 1.247576 −0.752060−0.302196 −0.788983 −0.113122 −0.325356 −0.054462 −0.573961 −0.098934−0.579122 −0.497202 −0.471776 −0.396048 −0.294917 −0.133438 −0.433938−0.245088 −0.132847 −0.742015 −0.122253 −0.604949 −0.068657 −0.075472−0.060983 −0.445207 −0.382346 −0.652673 −0.302064 −0.494450 −0.166497−0.233502 −0.196116 −0.340897 −0.907567 −0.452354 −1.043922 −0.158157−1.130081 −0.548716 −1.320594 −0.181413 −0.712483 −0.646623 −0.815526−0.865815 −1.157076 −0.928991 −1.532471 −0.508968 −0.120519 −0.915797−0.148259 −1.123784 −0.282652 −1.690100 −0.221465 −1.387236 −0.423824−0.821654 −0.488704 −1.037583 −0.872546 −1.413810 −0.675009 −1.247576;

and transmitting, by a transmitter of the wireless communication device,a wireless signal modulated in accordance with the constellationsymbols.
 16. The method of claim 15, wherein normalized magnitudes ofthe constellation symbols in the first quadrant of the 128-pointconstellation are defined by the coordinate pairs to at least fourdecimal places of precision.
 17. The method of claim 15, whereinnormalized magnitudes of the constellation symbols in the first quadrantof the 128-point constellation are defined by the coordinate pairs to atleast five decimal places of precision.
 18. The method of claim 15,wherein normalized magnitudes of the constellation symbols in the firstquadrant of the 128-point constellation are defined by the coordinatepairs to six decimal places of precision.
 19. The method of claim 15,wherein the constellation is a reflection-symmetric constellation. 20.The method of claim 15, wherein: left-hand-side coordinates of thecoordinate pairs represent normalized magnitudes of one of in-phasecomponents of the constellation symbols or quadrature components of theconstellation symbols; and right-hand-side coordinates of the coordinatepairs represent normalized magnitudes of the other one of the in-phasecomponents of the constellation symbols or the quadrature components ofthe constellation symbols.
 21. The method of claim 15, wherein the bitsequences are assigned to the constellation symbols using Gray mapping.22. An apparatus for a wireless communication device configured forwireless communication using digital quadrature amplitude modulation(QAM), the apparatus comprising: a mapping module electronic componentconfigured to translate between constellation symbols and bit sequencescorresponding to the constellation symbols in accordance with a128-point constellation; wherein normalized magnitudes of theconstellation symbols in a first quadrant of the 128-point constellationare defined by the following coordinate pairs to at least three decimalplaces of precision: 0.752060 0.302196 0.788983 0.113122 0.3253560.054462 0.573961 0.098934 0.579122 0.497202 0.471776 0.396048 0.2949170.133438 0.433938 0.245088 0.132847 0.742015 0.122253 0.604949 0.0686570.075472 0.060983 0.445207 0.382346 0.652673 0.302064 0.494450 0.1664970.233502 0.196116 0.340897 0.907567 0.452354 1.043922 0.158157 1.1300810.548716 1.320594 0.181413 0.712483 0.646623 0.815526 0.865815 1.1570760.928991 1.532471 0.508968 0.120519 0.915797 0.148259 1.123784 0.2826521.690100 0.221465 1.387236 0.423824 0.821654 0.488704 1.037583 0.8725461.413810 0.675009 1.247576 0.752060 −0.302196 0.788983 −0.1131220.325356 −0.054462 0.573961 −0.098934 0.579122 −0.497202 0.471776−0.396048 0.294917 −0.133438 0.433938 −0.245088 0.132847 −0.7420150.122253 −0.604949 0.068657 −0.075472 0.060983 −0.445207 0.382346−0.652673 0.302064 −0.494450 0.166497 −0.233502 0.196116 −0.3408970.907567 −0.452354 1.043922 −0.158157 1.130081 −0.548716 1.320594−0.181413 0.712483 −0.646623 0.815526 −0.865815 1.157076 −0.9289911.532471 −0.508968 0.120519 −0.915797 0.148259 −1.123784 0.282652−1.690100 0.221465 −1.387236 0.423824 −0.821654 0.488704 −1.0375830.872546 −1.413810 0.675009 −1.247576 −0.752060 0.302196 −0.7889830.113122 −0.325356 0.054462 −0.573961 0.098934 −0.579122 0.497202−0.471776 0.396048 −0.294917 0.133438 −0.433938 0.245088 −0.1328470.742015 −0.122253 0.604949 −0.068657 0.075472 −0.060983 0.445207−0.382346 0.652673 −0.302064 0.494450 −0.166497 0.233502 −0.1961160.340897 −0.907567 0.452354 −1.043922 0.158157 −1.130081 0.548716−1.320594 0.181413 −0.712483 0.646623 −0.815526 0.865815 −1.1570760.928991 −1.532471 0.508968 −0.120519 0.915797 −0.148259 1.123784−0.282652 1.690100 −0.221465 1.387236 −0.423824 0.821654 −0.4887041.037583 −0.872546 1.413810 −0.675009 1.247576 −0.752060 −0.302196−0.788983 −0.113122 −0.325356 −0.054462 −0.573961 −0.098934 −0.579122−0.497202 −0.471776 −0.396048 −0.294917 −0.133438 −0.433938 −0.245088−0.132847 −0.742015 −0.122253 −0.604949 −0.068657 −0.075472 −0.060983−0.445207 −0.382346 −0.652673 −0.302064 −0.494450 −0.166497 −0.233502−0.196116 −0.340897 −0.907567 −0.452354 −1.043922 −0.158157 −1.130081−0.548716 −1.320594 −0.181413 −0.712483 −0.646623 −0.815526 −0.865815−1.157076 −0.928991 −1.532471 −0.508968 −0.120519 −0.915797 −0.148259−1.123784 −0.282652 −1.690100 −0.221465 −1.387236 −0.423824 −0.821654−0.488704 −1.037583 −0.872546 −1.413810 −0.675009 −1.247576;

and a transmitter configured to transmit a wireless signal modulated inaccordance with the constellation symbols.
 23. The apparatus of claim22, wherein normalized magnitudes of the constellation symbols in thefirst quadrant of the 128-point constellation are defined by thecoordinate pairs to at least four decimal places of precision.
 24. Theapparatus of claim 22, wherein normalized magnitudes of theconstellation symbols in the first quadrant of the 128-pointconstellation are defined by the coordinate pairs to at least fivedecimal places of precision.
 25. The apparatus of claim 22, whereinnormalized magnitudes of the constellation symbols in the first quadrantof the 128-point constellation are defined by the coordinate pairs tosix decimal places of precision.
 26. The apparatus of claim 22, whereinthe constellation is a reflection-symmetric constellation.
 27. Theapparatus of claim 22, wherein: left-hand-side coordinates thecoordinate pairs represent normalized magnitudes of one of in-phasecomponents of the constellation symbols or quadrature components of theconstellation symbols; and right-hand-side coordinates of the coordinatepairs represent normalized magnitudes of the other one of the in-phasecomponents of the constellation symbols or the quadrature components ofthe constellation symbols.
 28. The apparatus of claim 22, wherein thebit sequences are assigned to the constellation symbols using Graymapping.